Question 1.
Define standard costing.
The estimated incomes and expenses for a particular period of time is called standard cost. According to ICMA the standard cost is.” A predetermined cost, which is calculated from management standards or efficient operation and the relevant necessary expenditure, it may be used as a basis for price fixing and for cost control through various analysis,

Question 2.
What is standard costing?
A Procedure or method for selling the predetermined cost estimation for providing a basis for comparing with the actual cost is called standard costing. According to ICMA. UK, Standard costing is.” The preparation and use of standard cost; their comparison with actual cost and analysis of variances to their causes and points incidence.

Question 3.
State any four steps involved in standard costing.
A Procedure or method for selling the predetermined cost estimation for providing a basis for comparison with actual cost is called standard cost. Its steps are:

1. Determination of standard Cost
2. Recording of actual cost.
3. Comparison the standard cost with actual cost.
4. Reporting about variance and taking corrective measure.

Question 4.
What do you mean by variance?
A variance means a deviation. A variance occurs when actual costs differ form standard costs. Variance Analysis is a study of such variances, and it involves not only measurement of variances, but also examination of the causes for the variance, explaining clearly the contribution of each cause or factor to the overall variance.

Question 5.
What is labour variance?
Labour variances arise when actual labour cost; are different from standard labour costs Labour variances involve calculation of Labour cost variance, Labour Rate Variance, labour time (or Efficiency) Variance, idle time variance and Labour mix or gang Composition Variance.’ A positive variance is favourable and denoted by A negative variance is adverse and is denoted by (A).

Question 6.
What is material cost variance?
It is difference between the standard costs for the output achieved and actual cost incurred for achieving the same. It is calculated with the help of the formula
MCV = (SQ × SP) – (AQ) where
SQ = Standard Quantity for Actual, output
SP = Standard price
AQ = Actual quantity used
AP = Actual price

Question 7.
What is material variance?
Material involve calculation of Material cost variance, Material price variance, Material usage variance material mix variance and material sub usage variance.

Question 8.
Give the meaning of Material usage variance.
Material Usage Variance explains the variance in material cost caused on account of the difference between the standard quantity specified and the actual quantity used. It a calculated as
MUV = MQV = SP × (SQ – AQ)
Material price Variance and Material usage Variance total up to material cost Variance i.e. MCV = MPV + MUV

Question 9.
What is labour yield variance?
The output obtained will not only be on account of material used but it will also be influenced by the efficiency of the labour working on the material. As such, Yield Variance can be calculated to know whether the output is as per the standard specified not. It is calculated as
LYV = Standard yield Rate (Actual Yield – Revised Standard Yield)
Where Standard Yield Rate = $$\frac{Total of RH × SR }{Revised Standard Yield}$$

Question 10.
Classify different type of direct material cost variance. Question 11.
Differentiate between favourable and unfavourable variance.
A variance is favourable if standard cost > Actual cost
Whereas, a variance is unfavourable, or adverse if actual cost > Standard cost.

Question 12.
What is material mix variance of why does it arise?
The differences between the standard mix specified and the actual mix, used is called. material mix variance. The causes for arising the material cost variance.

1. Increase in demand for particular variety of material.
2. Increase or decrease or price or any parties has material.
3. Change in the composition or materials etc.

Question 13.
What are the causes for material usage variance
The differences between standard quantity and the actual quantity used is material usage. The causes are as follows.

1. Uneconomical use of materials
2. carelessness in the use of materials
3. Use of substitute materials

Question 14.
A product X requires 25 units of standard material at the rate of ₹ 5 per unit.
The actual consumption of material for the manufacture of product X is 20 units at the rate of ₹ 4 per unit. Calculate material cost variance.
Calculation of material variance cost:
= Standard material cost – Actual material cost
= (25 units × ₹ 5/unit) – (20 units × ₹ 4/unit)
= ₹ 125 – ₹80 = ₹45

Question 14.
What are the causes of labour rate variance.
The causes of labour variance are given below.

1. Changes in basic wages rate,
2. Use of different methods of wage payment
3. Unscheduled overtime.
4. Poor working condition.
5. Machine Breakdown.
6. Increase in labour turnover.

Question 1.
What is standard cost ? Explain in brief the steps involved in it.
A method or procedure for selling the predetermined cost estimation for providing a basis for comparing with actual cost is called standard costing.

According the institute of management according in UK the standard costing is” The preparation and use of standard cost, their comparison with actual cost and analysis of variances to their causes and points incidence.

According to the institute of cost and works accountants London, the standard costing is defined as ” An estimate, cost, prepared in advance of production or supply correlating a technical specification of material and labour to the price and wages rates estimated for a selected period of time, with an addition of the apportionment of over hand expense estimated for the same period within a prescribed set of working conditions”

Through following steps standard costing may be prepared.
i) Estimating the standard cost.
ii) Recording of actual cost
iii) Comparing the actual cost with standard cost.
iv) Finding out of variances
v) Reporting about variance and taking necessary steps to corrective measure.

i) Estimating the standard cost: There is the first step of standard cost which helps to determine the standard cost on the basis of previous years finance, informations.

ii) Recording of actual cost: Then we have to record the actual cost for current. year, which is the present year data what ever performance in the current year.

iii) Comparing the actual cost with standard cost: Whatever information recorded in current year that is for financial performance of current year to king out the variances you should compare with the actual cost and standard cost.

iv) Finding out of variances: After comparing the actual cost with standard cost we will get the variances of them which help to know the position of current year comparing to previous year.

v) Recording the variances and taking a corrective measure: Whatever variances we got by comparing the current year actual cost with standard cost on the basic of that we have a find out the reasons of variances and should take a corrective measure to solve these problems.

Question 2.

 Advantages Disadvantages 1. Effective cost control 1. System may not be appropriate to the business 2. Helps in planning 2. Staff may not be capable to operate 3. Provides incentives to the employees 3. Business may not revise standards 4. Aid: management in determining price and formulating production policy 4. Inaccurate and unreliable standards cause misleading results 5. Reduces waste 5. Costly affair- small firms cannot afford it 6. Economic and simple 6. Costly

Question 3.
State the reasons for about efficiency variances.
(i) Machine breakdown, use of defective machinery and equipment.
(ii) Inferior raw materials
(iii) Poor supervision
(iv) Lack of timely material handling
(v) Poor employee performance
(vi) Inefficient production scheduling – delays in routing work; materials, tools and instructions
(vii) Inferior engineering specifications.
(viii) New inexperienced employees
(ix) Insufficient training of workers
(x) Poor working conditions – inadequate or excessive heating, lighting, ventilation etc.

Question 4.
From the following information, compute:
a) Material cost variances
b) Material price variance, and
c) Material usage variance
Standard quantity of materials per unit — 4000 kgs
Standard price per kg. of materials — ₹ 50.00
Actual production — 1000 units
Materials actually used — 4300 kgs
Actual purchase price of materials per kg — ₹ 55.00
a) Material cost variance = (Standard quantity × Standard price) – (Actual quantity × Actual price)
= (4,000 × 50) – (4,300 × 55) = (2,00,000 – 2,36,500) = ₹ 36,500 (Unfavourable)

b) Material price variance:
= (Actual quantity × Standard price) × (Actuat quantity × Actual price)
= (4,300 × 50) – (4,300 × 55) = 2,15,000 – 2,36,500 = ₹ 21,500 (Unfavourable)

c) Material usage variance: – MCV – MPV = 36500 – 21500 = 15,000 (Unfavourable)

Question 5.
From the following particulars calculate:
(i) Material cost variance
(ii) Material price variance
(iii) Material usage variance
Quantity of material purchased — 12,000 units
Value of material purchased — ₹ 36,000
Standard quantity of material
Required per unit of finished output — 12 units
Standard price of material — ₹ 10 per unit
Closing stock of material — 5,000 units
Finished output during the year — 320 units
(a) Materials cost variance = Standard cost for actual operation – Actual cost
= (320 × 30 × 10) – (2,500 × 3)
= 96,000 – 22,500 = 73,500 (F)
(₹ 3 is 36,000 7. 12,000)

(b) Materials price variance= (Std. rate – Actual rate) Actual quantity
= (10 – 3) 7,000
= 7 × 7,000 = 49,000

(c) Materials usage variance = (Std. Quantity – Actual quantity) × Std. Price
= (320 × 12) – 7,000) × 10
= 3,840 – 7,000 × 10
= -3,160 × 10 = 31,600 (A)

Question 6.
From the following particulars calculate material variances”
Quantity of materials purchased — 3,000 units
Value of materials purchased — ₹ 9,000
Standard quantity of materials required per ton of output — 30 units
Standard rate of materials — ₹ 2.50 per unit
Closing stock of materials — 500 units
Output during the period — 80 tons
(a) Materials cost variance = Standard cost for actual operation – Actual cost
= (80 × 30 × 2.5) – (2500 × 3)
= 1,500 (A)

(b) Materials price variance= (SP – AP) (AQ)
= (2.5 – 3) (2,500)
= 1,250 (A)

(c) Materials usage variance = (SQ – AQ) SP
= (2,400 – 2,500) 2.5 = 250 (A)

Question 7.
The standard material required for producing 100 units is 120 kgs.
A standard price of ₹ 0.50 per kg is fixed and 2,40,000 units were produced during the period. Actual materials purchased were 3,00,000 kgs, at a cost of ₹ 1,65,000.
Calculate:
a) Material cost variance
b) Material usage variance
Given Standard Price. = ₹ 0.50 per kg. Actual quantity = 3,00,000 kgs.
For producing 100 units is 12 kgs
For producing 2,40,000 units is ?
2,40,000 × $$\frac{120}{100}$$ = 2,88,000
Standard quantity = 2,88,000
Actual price = $$\frac{Actual cost}{Actual usage}$$ = $$\frac{1,65,000}{3,00,000}$$ = Rs.0.55

a) Material cost variance
= [Standard Quantity for actual output × Standard price] – [Actual quantity × Actual Price]
= [2,88,000 × 0.50] – [3,00,000 × 0.55]
= 1,44,000 – 1,65,000 = 21,000 (adverse)

b) Material usage variance
= [Standard quantity for actual output – Actual quantity] × Standard Price
= [2,88,000 – 3,00,000] × 0.50
= -12,000 × 0.50. = 6,000 (adverse)

Question 8.
The standard materials required for production 100 units to 120 kgs.
A standard price of 0.50 price per kg. is fixed and 2,40,000 units were production during the period. Actual material purchased were 3,00,000 kgs. At a cost of ₹ 1,65,000
Calculate:
i) Material cost variance
ii) Material price variance
iii) Material usage variance
Given, Standard price rate (SP) = 0.5 per kg
Standard quantity for producing 240000 (Actual) units
100 units production standard quantity = 120 kgs
(-)1 units production standard quantity = 20 kgs
100 kgs
24,000 units production standard quantity = $$\frac{120 \times 2,40,000 \mathrm{kgs}}{100}$$ = 2,88,000 kgs
Actual price rate = $$\frac{\text { Actual cost }}{\text { Actual usage }}$$ = $$\frac{1,65,000}{3,00,000}$$ = 0.55 paise.

a) Material cost variance:
= (Standard usage × Standard rate) – (Actual usage × Actual rate)
= (2,88,000 × 0.5) – (3,00,000 × 0.55) = 1,44,000-1,65,000 = ₹21,000 (unfavourable)

b) Material price variance:
(Actual quantity) × ( standard rate – Actual rate)
3,00,000 × (0.5 – 0.55) = 3,00,000 × (-0.05) = ₹ 15,000 (unfavourable)

c) Material usage Variance:
= Standard price rate (Standard usages – Actual usages)
= 0.5(2,88,000 – 3,00,000) = 0.5 × (-12,000) = ₹ 6,000 (unfavourable)

Question 9.
The Standard Material required to manufacture one unit of product A is 15 kgs
And the Standard Price of material per kg of material is ₹ 20. The cost accounts records however, revealed that 11,000 kgs. of materials costing ₹ 2,64,000 were used for manufacturing 1,000 units of Product A.
Calculate material variances.
Material cost variance = Std. cost – Actual cost
= 15 × 20 – 11 × 24
= 300 – 264 = 36 (F)
Actual price = $$\frac{2,64,000}{11,000}$$ = 24 Actual quantity= $$\frac{11,000}{1,000}$$ = 11 units Material price variance, = (Std. price – Actual price) Actual quantity
= (20 – 24) 11,000
= -4 × 11,000 = 44,000 (A)
Material usage variance = (Std. quantity – Actual quantity) Std. Price
= Std. quantity = 15 × 1000 units = 15,000 kg.
= (15,000 – 11,000) 20
= 4,000 × 20 = 80,000 (F).

Question 10.
The standard material required to manufacture one unit of product ‘X’ is 10 kgs and the standard price per kg of material is ₹ 25.
The cost accounts records, however reveal that 11,500 kgs materials costing ₹ 2,76,000 were used for manufacturing 1,000 units of Product ‘X’. Calculate Material variances.
ST usage for actual output of 1,000 units @ 10 kgs each = 10,000 kgs
actual price of the material per kg= ₹ 2,76,000/11,500 kgs = ₹ 24
a) Material cost variance = Standard cost of material less Actuall cost of material
10000 kg × ₹ 25 – 11,500 kgs × ₹ 24 = ₹ 26,000 adverse

b) Material price variance =. Actual usage (ST unit price – Actual unit price)
11,500 kgs (₹ 25 – ₹ 24) = ₹ 11,500 Favourable

c) Material usage variance = .ST unit price (ST usage-Actual usage)
₹ 25 (10,000 kg – 11,500 kgs) = ₹ 37,500 adverse.
Verification
MCV = MPV + MUV
₹ 26,000 adverse = 11,500F (₹ 37,500 adverse) = ₹ 26,000 A = ₹ 26,000 A

Question 11.
Using the following information calculate :
i) Labour cost variance.
ii) Labour rate variance and
iii) Labour efficiency variance :
Standard hours : 4,000
Actual hours : 5,000
Standard wage rate : ₹ 3 per hour
Actual wage rate : ₹ 2.50 per hour
i) Labour Cost Variance = (Std. Rate × Std. time)
= (Actual Rate × Actual time)
= (4,000 × 3)
= (5,000 × 2.5).
= 12,000 – 12,500 = 7.500 (unfavourable)

ii) Labour Rate Variance = Actual time (Std. Rate – Actual Rate)
= 5,000 (3 – 2.50)
= 5,000 × 0.50 = ₹ 2,500 (Favourable)

iii) Labour Efficiency variance = Std. Rate (Std. time – Actual time)
= 3(4,000 – 5,000)
= 3 × 1000 = ₹ 3,000 (unfavaurable)

Question 12.
From the following, calculate labour variances of department A
Dept. A
Actual direct wages — ₹ 2,000
Standard hours — 8,000
Standard rate per hour — 30 paise
Actual hours worked —8,200
LCV = Standard cost – Actual cosť
8,000 × 0.30 – 2,000 = 2,400 – 2,000 = 400 (f)
LRV = (SR – AR) × AH
(0.30 – 0.24) × 8,200 = 0.06 × 8,200 = 492 (f)
LEH = (SH – AH) × SR
= (8,000 – 8,200) × 0.30 = -200 × 0.30 = 60 (A)

Question 13.
The following information is obtained from a standard cost card.
Labour rate – ₹ 1.80 per hour
Hours – 4 hour per unit
Actual production data are:
Units produced – 400 units
Labour rate – ₹ 1.90 per hour
Hour worked – 1,500
Calculate:
a) Labour cost variance
b) Labour rate variance and
c) Labour efficiency variance
Given, Standard labour rate ₹ 1.80 per hour.
Standard time 4 hours per unit
∴ for 400 units = 4 × 400=1600 hours
Actual rate 1.90 per hours
Actual time = 1,500 hours

a) Labour cost variance::
= (Standard rate × Standard time – Actual time × actual. rate)
= (1,600 × 1.80 – 1,500 × 1.90)
= (2,880 – 2,850) = ₹ 30 (Favourable)

b) Labour rate variance
= Actual time (Standard rate – Actual rate)
= 1,500 (1.80 – 1.90)
= 1,500 × (-0:1) = ₹ 150 (Unfavourable)

c) Labour efficiency variances
= Standard rate (Standard – Actual time)
= 1.80 (1,600 – 1,500)
= 1.80 × 100 = 180 (favourable)

Question 14.
Using the following information calculate
a) Labour cost variance
b) Labour rate variance
c) Labour efficiency variance
Standard hours = 4,000
Actual hours = 5,000
Standard wage rate = ₹ 3 per hour
Actual wage rate = ₹ 2.50 per hour.
a) Calculation of Labour Cost Variance Labour Cost Variance = [Standard hours for actual output × Standard rate per hour] – [Actual hours × Actual rate per hour]
= [4000 × 3] – [5000 × 2.50]
= 12,000 – 12,500 = ₹ 500 (A)

b) Calculation of Labour rate Variance
Labour rate Variance = [Standard rate – Actual rate] × Actual hours
= [3 – 2.5] × 5000 = (0.5 × 5,000) = ₹ 2,500 (F)

c) Calculation of Labour efficiency variance
Labour efficiency variance : [Standard hours for actual output – Actual hours] × Standard rate
= [4,000 – 5,000]3 = (-1,000]3 = ₹ 3,000 (A)

Question 1.
A manufacturing concern which has adopted standard costing furnished the following informations:
Material 50 kgs, Finished products 100 kgs, Price of materials ₹ 2 per kg Actual: Output 18,000 kgs, Materials used 24,000 kgs, Cost of materials 21,000 kgs
You are required to calculate :
(i) Materials cost variance
(ii) Material price variance
(iii) Material usage variance
Standard quantity = $$\frac{Actual output × Std. finished produces }{Standard usages}$$
= $$\frac{18,000 \times 100}{50}$$ = 36,000 kgs
Actual cost = $$\frac{Cost material × price}{Quantity used}$$ = $$\frac{21,000 \times 2}{24,000}$$ = 1.75

a) Material cost variance= (SQ × SO) – (AQ × SP)
= (36,000 × 2) – (24,000 × 1.75)
= 72,000 – 42,000 = 30,000 ₹ (Favourable)

b) Material price variance = AQ × (SP – AP)
= 24,000 (2 – 1.75) = 6,000 Rs (favourable)

c) Material usage variances = SP(SQ – AQ) = 2(36,000 – 24,000)
= ₹ 24,000 (Favourable)

Question 2.
The standard mix to produce one unit of product is as follows:
Material A 60 units at ₹ 15 per unit = 900
Material B 80 units at ₹ 20 per unit = 1,600
Material C 100 units are ₹ 25 per unit = 2,500
Total = 5,000
During the month of April 100 units were actually produced and consumption was as follows:
Material A 6400 at 17.50 per unit = 1,12,000
Material B 9500 at 18.00 per unit = 1,71,000
Material C 8700 at 27.50 per unit = 2,39,250
24600 units = 5,22,250
Calculate all material variances.
A. Calculation of the Standard Quantity
Std. Qty. = $$\frac{Materials for one unit}{Materials/Product produced}$$Materials/Product produced × Actual output
= $$\frac{240 \text { units }}{1 \text { Product }}$$ × 100 products = 24,000 units

 Materials required for 100 units Actual yield Standard yield (a) Std. Qty = 24,000 units 100 Units 1/240×24,600 = 102.50 units (b) Actual Qty = 24,600 units

B. Material cost variance:
= Standard cost – Actual cost
= (5000/unit × 100 units) – (5,22,250) = ₹ 22,250 (A)

C. Material price variance:
Actual Quantity (Standard Price – Actual price)
Material A = 6400 (15 – 17.50)
= 6400 (-2.50) = ₹ 16,000 (A)
Material B = 9500 (20 – 18)
= 9500 (+2) = ₹ 19,000 (F)
Material ₹ = 8700 (25 – 27.50)
= 8700 (-2.50) = ₹ 21,750 (A)
∴ Material price variance (A + B + C) = ₹ 18,750 (A)

D. Material usage variance:
Standard Price (Standard Quantity – Actual Quantity)
Materials A = ₹ 15 (60/unit × 100 units – 6400)
= ₹ 15 (-400) = ₹ 6,000 (A)
Material B = ₹ 20 (80/unit × 100 unit – 9500)
= ₹ 20 (-1500) = ₹ 30,000 (A)
Material C = ₹ 25 (100 units × 100 units – 8700)
= ₹ 25 (1300) = ₹ 32,500 (F)
∴ Material usage variance (A + B + C) = ₹ 3,500 (A)

E. Material mix variance:
Revised standard Qty.
A = $$\frac{60}{240}$$ × 24,600 = 6150 units
B = $$\frac{80}{240}$$ × 24,600 = 8200 units
C = $$\frac{100}{240}$$ × 24,600 = 10250 units
Standard {price (Revised Std. Qty – Actual Qty)
Material A = ₹ 15 (6150 – 6400) = ₹ 3,750 (A)
Material B = ₹ 20 (8200 – 9500) = ₹ 26,000 (A)
Material C = ₹ 25 (10250 – 8700) = ₹ 38,750 (F)
∴ Material mix variançe (A + B + C) = ₹ 9,000 (F)

F. Material yield variance:
Standard rate (Actual yield – Standard yield)
= Standard Rate = $$\frac{Standard cost of standard mix}{Standard O/P}$$
= ₹ 5,000 = $$\frac{1}{240}$$ × 24600 = 102.50 units
= ₹ 5,000 (100 – 102.50)
= ₹ 12,500 (A)

Question 3.
The following information relates to a manufacturing company

 Budgeted Actual Output in units 12,000 14,000 No. of working days in a month 20 2 Fixed overheads ₹ 36,000 ₹ 49,000 Variable overheads ₹ 24,000 ₹ 35,000

There was an increase of 5% capacity
Calculate:
(vi) Capacity variance
7,000 + 7,000 = 14,000 ₹

(ii) Fixed overhead expenditure = Actual overhead cost – (actual units x standard ratio)
= – (14000 × $$\frac{36,000}{12,000}$$) + 49,000
= – (14,000 × 3) + 49,000 = – 42,000 + 49,000
= ₹ 7,000 = Total fixed overhead expenditure

(iii) Variable overhead expenditure variance = Actual variable overhead cost – Actual unit × Standard variable ratio)
= 35,000 – (14,000 × $$\frac{24,000}{12,000}$$) = 35,000 – 14,000 × 2 = ₹ 7,000

= 49,000 – 36,000 = ₹ 13,000

= Standard fixed rate × (Actual output-standard output)
= 3 × (14,000 – 12,000)
= 3 × 2000 = 6,000₹

(vi) Capacity variance
= Standardi ratio × (Reserve budgeted units-Budgeted units)
= 3 × (12,600 – 12,000) = 3 × 600 = ₹ 1800
Reserve budgeted units = (Budgeted units + increase capacity)
= 12,000 + 5% of 12,000 = 12,000 + 600,= 12600 units

Question 4.
The following details are available from the records of ABC Ltd., engaged in manufacturing article ‘A’ for the week ended 28th September.

 Hours Rate per hour ₹ Total ₹ Skilled labour 10 3.00 30 Semi-skilled labour 8 1.50 12 Unskilled labour 16 1.00 16 58

The actual production was 1,000 articles of ‘A’ for which the actual hours worked and rates are given below:

 Hours Rate per hour ₹ Total ₹ Skilled labour 9,000 4-0 36,000 Semi-skilled labour 8,400 1-50 12,600 Unskilled labour 20,000 0-90 18,000 66,600

From the above set of data you are asked to calculate:
a) Labour cost variance
b) Labour Rate Variance
c) Labour Efficiency variance
d) Labour Mix Variance
a) Labour Cost Variance:
= (Std. hours for Actual production × S.R.) – (AH × AR)
Std. hours for Actual production = Actual units × SH
Skilled workers = 1000 × 10 = 10,000
Unskilled workers = 1000 × 16 = 16,000
Semi – Skilled workers = 1000 × 8 = 8,000
Labour cost Variance:
Skilled Workers = (10,000 × 3) – (9,000 × 4)
= 30,000 – 36,000 = ₹ 6,000
Unskilled workers = (16,000 × 1) – (20,000 × 0.9)
= 16,000-18,000 = ₹ 2,000
Semi skilled worker : = (8,000 × 1.50) – (8,400 × 1.5).
= 12,000 – 12,600 = ₹ 600
Total labour cost variance = 8,600 ₹

b) Labour price variance = AH (SR – AR)
Skilled workers = 9,000 (3, – 4) = ₹ 9,000
Semi skilled workers = 8,400 (1.50 – 1.50) = Nil
Unskilled workers = 20,000 × (1 – 0.90) = 20,000 × 0.1 = 2000(F)
Total labour price variance = ₹ 7,000 (A)

c) Labour mix Variance
SR (Revised std. mix of Actual hours worked) – Actual mix
Revised std. mix of Actual work = $$\frac{Std. mix }{Total std hours}$$
Skilled workers = $$\frac{10,000}{34,000}$$ × 37,400 = 11,000
Semi skilled workers = $$\frac{8,000}{34,000}$$ × 37,400 = 8,800 ₹
Unskilled workers = $$\frac{16,000}{34,000}$$ × 37,400 = 17,600 ₹
Labour mix Variance
Skilled workers = 3. (11,000 – 9,000) = ₹ 6,000 (F)
Semi Skilled workers = 1.50 (8,800 – 8,400) = ₹ 600 (F)
Unskilled worker = 1.00 (17,600 – 20,000) = ₹ 2,400 (A)
Total Labour mix variance = ₹ 4,200 (F)

d) Labour Efficiency variance = SR (SH for Actual production – Revised std. Hr’s)
Skilled workers = 3 (10,000 – 11,000) = ₹ 3,000 (A)
Semi Skilled workers = 1.50 (8,000 – 8,800) = ₹ 1,200 (A)
Unskilled workers = 1.00 (16,000 – 17,600) = ₹ 1,600 (A)
Total labour Efficiency variance = ₹ 5,800 (A)

Question 5.
The standard materials required for producing 200 units is 250 kgs.
A standard price of 0.60 praise per kg. 2,50,000 units were produced during the period. Actual materials purchased were 3,20,000 kgs at a cost of ₹ 1,95,200.
From the above, calculate:
(a) Material cost variance
(b) Material price variance and
(c) Material usage variance
Standard quality For 200 finished units required 250 kgs raw materials
2,50,000 finished units required 250 kgs raw materials = $$\frac{250 \times 2,50,000}{200}$$
= 3,12,500 kgs
Actual price for kg = $$\frac{1,95,200}{3,20,000}$$ = 0.61 paise

a) Material Cost Variance
(Standard material cost – Actual Material cost)
= (3,12,500 × 0.60) – (3,20,000 × 0.61)
= 1,87,500 – 1,95,200 = ₹ 7,700 (Unfavourable)

b) Material price variance
(Actual quantity × (Standard price – Actual price)
= (3,20,00 × (0.60 – 0.61).
= 3,20,000 × (-0.01) = ₹ 3,200 (Unfabourable)

c) Material usage variance
(Standard price × (Standard quantity – Actual quantity)
= 0.60 × (3,12,500 – 3,20,000
= 0.60 × (-7,500) = ₹ 4,500 (Unfavourable)

Question 7.
The standard cost for a product shows:
Material cost 2 kg at ₹ 3 each ₹ 5 per unit wages 3 hours at ₹ 1.50 each ₹ 2 per unit.
The actual which have emerged from business operations are as follows:
Product 8,000 units, Material consumed 15,000 kg at ₹ 2 each ₹ 30,000 wages paid 22,000 hours at ₹ 0.50 each ₹ 11,000 Calculate material and labour variance.
Given Standard quality = (2 × 8,000) = 16,000
Actual quantity = 15,000
Standard price = ₹ 3 per. unit
Actual rate = ₹ 2. per unit
Now, Material cost variance
= (standard quantity × Std. price) – Actual quantity × Actual prise)
= 16,000 × 3) – (15,000 × 2)
= 48,000 – 30,000 = 18,000 (Favourable)
Material price variance = Actual quantity (Std. Price – actual price)
= 15,000 (3 – 2) = 15,000 (favourable)
Material wages variance = Standard price (Std. quantity – Actual quantity)
= 3 (16,000 – 15,000) = 3,000 (Favourable)
Again,
Standard labour hour = (3 × 8,000) = 24,000
Actual labour hour = 22,000
Std. rate = 1.50 ₹
Actual rate = ₹ 0.50
Now,
Labour cost variance
= (Std. hour × Std. rate) – (Actual hour × Actual Rate)
= (24,000 ₹ 1.50) – (22,000 ₹ 0.5)
= (36,000 – 11,000) = ₹ 25,000
Labour rate Variances = Actual hour (Std. Rate – Actual rate)
= 22,000 (1.5 – 0.5) = 22,000
Labour efficiency variance = Std. rate (Std. hour – Actual rate)
= 1.5 (24,000 – 22,000)
= (1.5 × 2,000)
= ₹ 3,000

B.Com 1st Sem Financial Accounting Questions and Answers

Unit 1 Theoretical Framework of Financial Accounting

• Theoretical Framework of Financial Accounting Very Short Answer Questions
• Theoretical Framework of Financial Accounting Short Answer Questions
• Theoretical Framework of Financial Accounting Long Answer Questions

Unit 2 Conversion of Single Entry Into Double Entry System

• Conversion of Single Entry Into Double Entry System Questions and Answers

Unit 3 Hire Purchase Accounting

• Hire Purchase Accounting Questions and Answers

Unit 4 Departmental Accounts

• Departmental Accounts Questions and Answers

Unit 5 Branch Accounts

• Branch Accounts Questions and Answers

B.Com 1st Sem Financial Accounting Notes

B.Com 1st Sem Financial Accounting Syllabus

Unit 1: THEORETICAL FRAMEWORK OF FINANCIAL ACCOUNTING (08 Hrs)
Introduction – Meaning and Definition – Significance of Accounting – Functions of Accounting- Users of Accounting Information – Accounting Principles – Accounting Concepts and Accounting Conventions- Accounting equations, Problems on Accounting Equations – Accounting Standards: List of Indian Accounting Standards.

Unit 2: CONVERSION OF SINGLE ENTRY INTO DOUBLE ENTRY SYSTEM (12 Hrs)
Need for Conversion – steps in conversion- ascertainment of capital- total sales- total purchases – Cash and bank balances – stock – Bills Receivable – Bills payable -Preparation of Final accounts – Trading and Profit & Loss Account and Balance Sheet.

Unit 3: HIRE PURCHASE ACCOUNTING (12 Hrs)
Meaning of Hire Purchase and Instalment Purchase System- Hire Purchase v/s sale – differences between Hire Purchase and Instalment system, the meaning of Some important technical terms – Hire Purchase Agreement – Hire Purchase Price – Cash Price – Hire Purchase Charges – Net Hire Purchase Price – Net Cash Price – Calculation of Interest – Calculation of Cash Price – Journal Entries and Ledger Accounts in the books of Hire Purchaser and Hire Vendor (Asset Accrual Method only and excluding repossession).

Unit 4: DEPARTMENTAL ACCOUNTS (10 Hrs)
Meaning, Objectives, basis of apportionment of common expenses among different departments- Preparation of Trading and Profit and Loss Account in Columnar form-preparation of balance sheet in horizontal format – (Including Inter-Departmental Transfers at cost price only).

Unit 5: BRANCH ACCOUNTS (10 Hrs)
Introduction.- Meaning – Objectives – Types of Branches – Dependent Branches – Features – Supply of Goods at Cost Price – Invoice Price – Branch Account in the books of Head Office (Debtors System Only).

Question 1.
What do you mean by absorption costing?
It is total costing technique under which total cost is charged as production cost. Here all manufacturing costs are absorbed in the cost of the products produce. It is also known conventional costing or full costing.

Question 2.
Define Marginal costing.
According to CIMA it is “the accounting system in which variable costs are charged to cost units and fixed costs of the period are written off in full against the aggregate contribution. Its special value is in decision making.”

Question 3.
What is product cost?
Product cost are those cost which become a part of production cost.

Question 4.
What is period cost?
Period cost are those costs which are not incurred for production and are not included in the cost of product or stocks.

Question 5.
What is cost-volume-profit analysis?
CIMA, London has defined CVP analysis as “the study of the effects on future profits of changes in fixed cost, variable costs, sales price, quantity and mix”. It studies the inter relationship of three basic factors:

1. Cost of production
2. Volume of production or sales
3. Profit

Question 6.
What is contribution?
The differences between sales & variable cost is called contribution or the excess of sales over the variable cost is contribution
So Contribution = Sales – Variable cost

Question 7.
Write any two advantages of contribution.
The advantages of contribution are as follows:

1. It helps the management to control the cost as it classifies the fixed and variables.
2. It helps to management the relative profitability of product is based on a study of contribution made by each of product.

Question 8.
What is p/v ratio?
Contribution to sale ratio or profit value ratio is the proportion of contribution to sale. So the ratio of contribution to sale is called p/v ratio it is the percentage on sale.
P/v ratio = $$\frac{\text { Contribution }}{\text { Sales }}$$ × 100

Question 9.
Give the meaning of fixed cost with an example.
A fixed cost is an expense that does not change as production volume increases or decreases within a relevant range. In other words, fixed costs are locked in place as long as operations stay within a certain size.

Question 10.
How can piv ratio be improved?
P/V Ratio is the relationship between the profit & sales. In formula it is expressed as P/V Ratio= Contribution/sales*100.
The higher the P/V Ratio better is for company prospects.

Question 11.
State the features of profit volume ratio.

1. It makes relationship between contribution and sales.
2. Its help to calculate profitability of the business.

Question 12.
What is break even analysis?
The procedure to find out the break even point is called break even analysis, so it is the system which helps to find out a probable level of output where the total cost= total revenue.

Question 13.
What is break even point?
Break even point can be written as BEP. It is a point of production level where all the expenses are equal to all the revenue. It means at breakeven point, there is no loss or gain.

Question 14.
Expand BEP.
BEP stand for Break Even Point which indicates the production level where the total sales become equal to total cost BEP = Total cost – Total sales = 0

Question 15.
What is break-even chart?
Chart where sales revenue, variable costs, and fixed costs are plotted on the vertical axis while volume is plotted on the horizontal axis. The break-even point is the point where : the total sales revenue line intersects the total cost line. Question 16.
What do you mean by margin of safety?
The breakeven Sales are known as margin of safety. The differences between actual sales and sales of Break even is called margin of safety, it may be called sales over.
Margin of safety Actual sales-sales at Break even point.

Question 17.
Define angle of incidence.
Transaction of sales line and total cost line at the break even point is called angle of incidence. These angle shows, the rate of profit earning rate on the breakeven point when it has been reached. The rate of earning profit at a wider angle is greater angle.

Question 18.
What are non operating incomes and expenses?
Non business operational increase & decrease of income & expenses are called non operational income & expenses.

Question 19.
What is trend analysis?
Another name of trend analysis is trend ratio, which refers to ascertaining the arithmetical relationship among each items of several years, to the same items of base year. It means one particular year out of many financial years, it is procedure of converting to ratio or percentage from one particular item out of several items shown in financial statement.

Question 20.
What is marginal cost equation?
MC = $$\frac{d T C}{d Q}$$
The marginal cost (MC) function is expressed as the derivative of the total cost (TC) function with respect to quantity (Q).

Question 1.
Discuss the argument for absorption costing.
1. Compliance with the generally accepted accounting principles.
2. Importance of fixed overheads for production.
3. Avoidance of fictitious profit or loss.

4. During the period of high sales, the production is small than the sales, a smaller number of fixed manufacturing overheads are charged and a higher net profit will be obtained under marginal costing.

5. Absorption costing is better in avoiding the fluctuation of profit being reported in marginal costing.

Question 2.
What are the characteristics of marginal costing?
The characteristics of marginal costing are:
(i) Segregation of costs into fixed and variable elements: In marginal costing, all costs are classified into fixed and variable elements.

(ii) Marginal costs as product costs: Only marginal (variable) costs are charged to products produced during the period.

(iii) Fixed costs as period costs: Fixed costs are treated as period costs and are charged to the costing profit and loss account of the period in which they are incurred.

(iv) Valuation of inventory: The work-in-progress and finished stocks are valued at marginal cost only.

(v) Contribution: Contribution is the difference between sales value and marginal cost of sales. The relative profitability of products or departments is based on a study of contribution made by each of the products or departments.

(vi) Pricing: In marginal costing, prices are based on marginal cost plus contribution.

Question 3.
Discuss the advantages of marginal costing.
The advantages of marginal costing are:
(i) Helps in managerial decision: It helps the management in making valuable decision by providing information regarding marginal cost and contribution.

(ii) Cost control: It helps the management to control the cost as it classifies the cost into ‘fixed and variables. This helps the management to concentrate more on the variable cost.

(iii) Simple technique: It is very simple to operate as it avoids allocation, apportionment and absorption of fix the overheads.

(iv) Aid to profit planning: It presents the data to the management in a such way so as to show the cost – volume – profit relationship. This facilitates planning future performance.

(v) Valuable adjunct to other techniques: It is a valuable adjust to standard costing and budgetary control.

Question 4.
Distinguish between absorption and marginal costing.

 Absorption Costing Marginal Costing 1. All costs (fixed & variable) are charged to product 1. Only variable costs are charged to the product and fixed cost are treated as period cost. 2. Stock is valued at total cost which includes both fixed and variable. 2. Stock of WIP and finished goods are valued at marginal cost. 3. Relative profitability is just by profit 3. Relative profitability is based on a study of relative contribution made by respective products or depts. 4. Profit acts as a guiding factor for managerial decisions 4. Contribution acts as a guiding factor for managerial decisions.

Question 5.
What are the assumptions and uses of break even analysis?
Assumptions of break even analysis:
i) It is frequently mistaken for the payback period, the time it takes to recover, an investment. There are variations on break even that make some people think we have it wrong. The one we do use is the most common, the most universally accepted, but not the only one possible.

ii) It depends on the concept of fixed costs, a hard idea to swallow. Technically, a break-even analysis defines fixed costs as those costs that would continue even if you went broke. Instead, you may want to use your regular running fixed costs, including payroll and normal expenses. This will give you a better insight on financial realities. We call that “burn rate” these post-Internet days.

iii) It depends on averaging your per-unit variable cost and per-unit revenue over the whole business.

iv) If company have the fixed and variable cost then it is possible to calculate it.

Uses of break even analysis:
i) Break even analysis allows the firm to determine at what level of operations it will break even (earn zero profit) and to explore the relationship between volume, costs, and profits.

ii) It helps the management that at current costs of products of how many number of units must be sold to recover the cost of producing the product.

iii) It also helps the management to determine how many units to be sold to get desired profit on product.

iv) The Break-even Analysis lets you determine what you need to sell, monthly or annually, to cover your costs of doing business–your break-even point.

v) The Break-even Analysis table calculates a break-even point based on fixed costs, variable costs per unit of sales, and revenue per unit of sales.

Question 6.
Given Sales is ₹ 12.50 Lakhs, variable costs are ₹ 10.03 lakhs, total loss ₹ 1.96 Lakhs. Find its Fixed cost.
Given, Sales = 12,50,000
Variable cost = 10,03,000
Loss = 19,6000
We know that,
Sales = Fixed cost + Variable cost – Loss
⇒ 12,50,000 = Fixed cost + 10,03,000 – 1,96,000
⇒ Fixed cost + 8,07,000 = 12,50,000
⇒ Fixed cost = 12,50,000 – 8,07,000
∴ Fixed cost = 4,43,000

Question 7.
Sales ₹ 1,50,000, profit ₹ 40,000 fixed cost ₹ 30,000. Calculate variable cost.
Given, Sales = 1,50,000
Profit = 40,000
Fixed cost = 30,000
we know
Sales = Fixed cost + Variable cost + Profit
Variable cost = Sales – Fixed cost – Profit
= 1,50,000 – 30,000 – 40,000..
=1,50,000 – 70,000 = 80,000
∴ Variable cost = 80,000

Question 8.
Variable cost ₹ 50,000, fixed cost ₹ 30,000 and profit 10.000 Calculate the value of sales.
Given, Variable cost = 50,000
Fixed cost = ₹ 30,000
Profit = ₹ 10,000
We know that
Sales = Fixed cost + Profit + Variable cost
= 30,000 + 10,000 + 50,000 = 90,000
∴ Sales = ₹ 90,000

Question 9.
Given sales ₹ 10,00,000, Variable cost ₹ 7,00,000 Loss 1,00,000 find fixed cost.
we know that
Sales = Fixed cost + Variable cost – Loss Fixed
cost = Sales – Variable cost + Loss
= 10,00,000 – 7,00,000 + 1,00,000
= 11,00,000 – 7,00,000 = 4,00,000
∴ Fixed cost = ₹ 4,00,000

Question 10.
Calculate the Break Even Point in units. Fixed cost ₹ 1,20,000, Variable cost per units ₹ 10, Selling price per unit ₹ 16.
BEP = $$\frac{Fixed cost}{Contribution}$$ = $$\frac{Fixed cost}{SPPU – VCPU}$$
= $$\frac{1,20,000}{16-10}$$ = $$\frac{1,20,000}{6}$$ = 20,000 units.

Question 11.
The following data relates to a firm:
Selling price per unit ₹ 20
Variable cost per unit ₹ 12
Fixed expenses ₹ 4,000
Calculate:
(a) P/V ratio
(b) BEP (in units) and in value
(c) New BEP (in units) and in value if selling price is reduced by 20%.

Question 12.
The following information relates to a firm:
Selling price per unit ₹ 200
Variable cost per unit ₹ 160
Fixed cost ₹ 6,00,000
Find out:
a) B.E.P. in units and in value
b) Find out the selling price per unit in B.E.P is brought down to 8000 units.

Question 13.
The following information in obtained from A Itd, for the year 1998
Sales — 60,000
Variable cost — 30,000
Fixed cost — 15,000
you are required to:
a) Calculate the P/v Ratio, Break even point and margin of safety at this level.
b) Calculate the effect of 10% increase in sales price

Question 14.
Given : Sales ₹ 5,00,000
Fixed Cost ₹ 1,00,000,
Variable-cost 3,00,000
Find out the following:
a) p/v. ratio
b) B.E.P.
c) Sales volume required to earn a profit of ₹ 90,000
d) Sales volume when there is a loss of ₹ 30,000

Question 15.
Sale of product amounts to 200 units per month at ₹ 10 per unit.
Fixed overhead is ₹ 400 per month and variable cost is ₹ 6 per unit. There is proposal to reduce prices by 10%. Calculate present and future P/V ratio. How many units must be sold to earn the present total profit?

Question 16.
Sales of a product amount to 200 units over month at ₹ 10 per unit.
Fixed cost is ₹ 400 per month and variable cost is 56 per unit. There is a proposal to reduce selling price by 10%. Calculate present and future P/V ratio. Also calculate the. BEP units and value.
When, sales per unit ₹ 10
Variable cost ₹6 per unit
∴ contribution = Sales – Variable cost
= 10 – 6 = ₹4
P/V ratio = $$\frac{Contribution}{Sales}$$ × 100 = $$\frac{4}{10}$$ × 100 = 40%
(BEP) (in units) $$\frac{Fixed Cost }{Contribution}$$ = $$\frac{400}{4}$$ = 100 units
BEP (in value) = $$\frac{Fixed Cost }{P/V ratio}$$ = $$\frac{400}{40%}$$ = $$\frac{400 \times 100}{40}$$ = ₹ 1000
When selling price is reduced by 10% P/V. ratio will be :
Selling price per unit = 9
∴ Contribution = (9 – 6) = 3
P/v ratio = $$\frac{Contribution}{Sales}$$ × 100 ⇒ $$\frac{3}{9}$$ × 100 = 33.33%

Question 17.
A firm has produced and sold 20,000 units during the year 2016. The selling price was 3:50 per unit. The cost details were: Direct material ₹ 6 per unit
Direct labour ₹ 6 per unit
Variable overhead ₹ 3 per unit
Fixed expenses ₹ 3,50,000
Prepare a marginal cost statement to show the profit or loss for the year and also find out the Break Even point.

Question 18.
The following figures of sales and profits for two periods are available in respect of a concern.

 Particulars Sales ₹ Profit ₹ Period 75,000 7,500 Period II 60,000 11,500

You are required to find out:
a) P/V ratio
b) Fixed cost.
P/V ratio = $$\frac{Change in Profit}{Change in sales}$$ × 100
= $$\frac{(11,500-7,500)}{(60,000-75,000)}$$ × 100 = $$\frac{4,000}{-15,000}$$ × 100 = -26.67%
Please note: There seems to be an error in this problem as p/v ratio can never be negative. Also, as per data given in period II, even though profits have increased, sales have come down and this is not possible.

Question 19.
An analysis of costs of a company led to the following information

 Variable cost (% of sales) Fixed cost (₹) Direct materials 33.6 – Direct labour 28.4 – Factory overhead 11.6 1,66,700 Distribution overhead 3.3 63,400 General administration overhead 1.1 99,900

Budgeted sales for the next year ₹ 20,00,000
You are required to determine:
a) Break even sales
b) Profit at the budgeted sales volume
c) Sales to generate a profit of ₹ 2,20,000
Total variable cost
Direct material — 33.6% on sales
Direct labour — 28.4% on sales
Factory over head — 11.6% on sales
Distribution over head — 3.3% on sales
— 78% on sales
Total fixed cost = 1,66,700 + 63,400 + 99,900 = 3,30,000
Contribution = Sales – Variable cost = (100 – 78)% = 22%
a) Break even point = $$\frac{\text { Fixed Cost }}{\mathrm{P} / \mathrm{v} \text { ratio }}$$ = $$\frac{3,30,000}{22 \%}$$ =$$\frac{3,30,000 \times 100}{22}$$ = ₹ 15,00,000
b) Profit, when budgeted sales of ₹ 2,00,000
Profit = Sales-Variable cost’ – Fixed cost
= 20,00,000 – (20,00,000 × 78/100) – 3,30,000
= 20,00,000 – 15,60,000 – 3,30,000
= 20,00,000- 18,00,000 = ₹ 1,10,000
c) When sales to generate a profit of ₹ 2,20,000
Here, Sales = $$\frac{Fixed cost + Desire profit}{P/ v ratio}$$
= $$\frac{3,30,000+2,20,000}{22 \%}$$ = $$\frac{5,50,000 \times 100}{22}$$ = ₹ 25,00,000

Question 20.
Lucky buckets sold 14,000 buckets and 18,000 buckets at ₹ 50 per bucket in two consecutive years.
The company incurred a loss of ₹ 10,000 in the first year and earned a profit of ₹ 10,000 in the second year. Find out:
a. Amount of Fixed Cost:
b. Break-even Point (Quantity) and
c. Sales required to earn a profit of ₹ 35,000

Question 21.
From the following particulars, calculate:
i) Break-even point in terms of sales value and in units.
ii) Number of units that must be sold to earn a profit of ₹ 90,000
Fixed factory overheads cost — ₹ 60,000
Fixed selling overheads cost — ₹ 12,000
Variable manufacturing cost per unit — ₹ 12
Variable selling cost per unit — ₹ 3
Selling price per unit — ₹ 24
Selling price per unit — 24
Less : Variable cost per unit (12 + 3) — 15
Unit contribution — 9
BEP in units = $$\frac{Fixed cost}{Unit contribution}$$ = $$\frac{72,000}{9}$$ = 8,000 units :
BEP in ₹ 8,000 × 24 = ₹ 1,92,000
Required sales in units = $$\frac{Fixed cost + Desired profit}{Unit contribution}$$ = $$\frac{72,000+90,000}{9}$$
= 18,000 unit

Question 22.
The following figures relate to one year work in manufacturing organisations:
Direct wages — 15,000
Direct materials — 41,000
Sales — 1,00,000
Find the break even point.
Total variable cost = (Variable overheads + Direct wages + Direct materials)
= (20,000 + 15,000 + 41,000)= ₹ 76,000
Fixed cost Sales-variable x Sales
ВЕР = $$\frac{\text { Fixed cost }}{\text { Sales-variable }}$$ × Sales
= $$\frac{12,000}{1,00,000-76,000}$$ × 1,00,000
= $$\frac{12,000}{24,000}$$ × 1,00,000 = ₹ 50,000

Question 1.
The following figures of sales and profits for two periods are available in respect of a concern:

 Sales (₹) Profit (₹) Period I 1,00,000 15,000 Period II 1,20,000 23,000

You are required to find out:
a) P/V ratio
b) Fixed cost
c) Break-even point
d) Profit at an estimated sale of ₹ 1,25,000
e) Sales required to earn a profit of ₹ 20,000
a) P/ Ratio = $$\frac{Change in profit}{Change in sales}$$ × 100
= $$\frac{23,000-15,000}{1,20,000-1,00,000}$$ × 100 = $$\frac{8,000}{20,000}$$ × 100 = 40%
b) Fixed cost = Sales × P/V ratio – Profit
= 1,00,000 × $$\frac{40}{100}$$ – 15,000 = 40,000 – 15,000 = ₹ 25,000
c) Break-even point (for sales) = $$\frac{Fixed Cost }{P/v Ratio}$$
= $$\frac{25,000}{40 \%}$$ = $$\frac{25,000}{40}$$ × 100 = ₹.62,500
d) Profit, at an estimated sale of ₹ 1,25,000
Profit = P/v ratio × sales – Fixed cost
= 40% × 1,25,000 – 25,000
= 50,000 – 25,000 = ₹ 25,000
e) Sales required to earn a profit of ₹ 20,000
Sales = $$\frac{Fixed cost + Desired profit}{P/V ratio}$$
= $$\frac{25,000+20,000}{40 \%}$$ = $$\frac{25,000+20,000}{40}$$ × 100 = ₹ 1,12,500

Question 2.
A Ltd, maintains, margin of safety of 37.5% with an overall contribution to sales ratio of 40%. It fixed costs amount to ₹ 5 lakhs. Calculate the following.
1) Break even sales.
2) Total sales.
3) Total variable cost.
4) Current profit.
5) Margin of safety.
6) What would be the impact of change in contribution sales ratio to 50%
7) New margin of safety if the sales value is increased by 71/2%

Question 3.
‘M’ Ltd manufactures and sells three products A,B,C with a sales mix of 331/3; %, 16 2/3% and 50% respectively.
The total budgeted sales during the month December 1999 is ₹ 2,00,000 (2000 units) The following are the operating costs:
Variable cost A 70% of Sales
B 60% of Sales
C 65% of Sales
Fixed cost ₹ 50,000
Calculate break even point for the products on an overall basis.
What will be the BEP if the sales mix is changed as follows: (With the total sales remaining at ₹ 2,00,000).
A-33 1/3%, B-33 1/3 %, C-33 1/3
Also prepare marginal cost statement.

Question 4.
A retail dealer in garment is currently selling 24.000 shirts annually. He supplies the following details for the year ended 31 Dec. 2001
Selling price per shirt — ₹ 40
Variable cost per shirt — ₹ 25
Fixed cost:
a) Salaries for the year — ₹ 1,20,000
b) General office costs for the year — ₹ 80,000
c) Advertising cost for the year — ₹ 40,000
From the above details:
a) Calculate the break-even point and margin of safety in sales revenue and number of shirts sold.
b) Assume that 20,000 shirts were sold in a year and find out the net profit of the firm.
c) If it is decided to introduce selling commission of 33 per shirt, how many shirts would require to be sold in a year to earn a net income of rs. 15,000.
d) Assuming that for the year 2002 an additional staff cost ₹ 33,000 is anticipated and price of a shirt is likely to be increased by 15%. What should be break even point in number shirts and sales volume?
Working note:
Selling price per unit — ₹ 40
Less: Variable cost per unit — ₹ 25
Contribution per unit — ₹15
Total Fixed cost:
Salaries for the year — 1,20,000
General office cost for the year — 80,000
Advertising cost for the year — 40,000
Total fixed cost — 2,40,000
a) BEP (in units) = $$\frac{2,40,000}{15}$$ = 16,000 shirts
BEP (sales volume) = 16,000 shirts × Selling price per shirt.
= 16,000 × 40 = ₹ 6,40,000
Margin of safety= Actual sales – B.Ę.P sales
= (24,000 × 40) – 6,40,000
= 9,60,000 – 6,40,000 = 3,20,000
Margin of safety in units = ₹ 3,20,000 ÷ 40 = 8,000 shirts

b) Net profit when 20,000 shirts are sold :
Contribution (20,000 × 15) = 3,00,000
Less: Fixed cost = 2,40,000
Profit = 60,000

c) If it is decided to introduce selling commission of ₹ 3 per shirt, how many shirts would require to be sold in a year to earn a net income of ₹ 15,000.
Sales required to a profit of ₹ 3 per shirt.
Revised contribution = ₹ 15 – ₹ 3 = ₹ 12 per shirt.
Desired sales = $$\frac{Fixed cost + Desired profit}{ Revised contribution per unit}$$ = $$\frac{2,40,000+15,000}{\text { Rs. } 12}$$ = 21,250
New B.E.P when additional staff cost of * 33,000 is incurred and selling price is increased by 15%. Revised Fixed Cost = 2,40,000 + 33,000 = 2,73,000
Revised selling price per shirt = 40 + 6 (i.e., 15% of 40)= 46 ₹
New B.E.P. in units = $$\frac{New Fixed cost }{New contribution per unit}$$
= $$\frac{2,73,000}{46-25}$$ = $$\frac{2,73,000}{21}$$ = 13,000 shirts
New B.E.P in amount = 13,000 shirts. × ₹ 46 = ₹ 5,98,000

Question 5.
An analysis of X Co. Ltd. led to the following information,

 Cost Element Variable cost (% of sales) Fixed Cost ₹ Direct material 32.8 – Direct labour 28.4 – Factory overheads 12.6 1,89,900 Distribution overheads 4.1 58,400 Administration overheads 1.1 66,700

Budgeted sales are ₹18,50,000 Your are required to determine:
i) The break-even sales volume
ii) The profit at the budgeted sales volume
iii) The profit if actual sales:
a) Drop by 10% and
b) Increase by 5% from budgeted sales
iv) The sales required to earn a profit of ₹ 1,00,000.
P/V ratio = $$\frac{Contribution}{Sales}$$ × 100
Contribution = Sales – Variable cost
Variable cost = 32.8. + 28.4 + 12.6. + 4.1 + 1.1 = 79% of sales
Hence, contribution = 21% of sales
P/V ratio = 21%
(i) BEP of sales = $$\frac{Fixed cost}{P/V ratio}$$
= $$\frac{3,15,000}{21 \%}$$ = $$\frac{3,15,000 \times 100}{21}$$ = 15,00,000

(ii) Profit at budget sales
Profit = Contribution – Fixed Assets
Contribution at sales ₹ 18,50,000
18,50,000 × $$\frac{21}{100}$$ = 3,88,500
∴ Profit = 3,88,500 – 3,15,000 = ₹ 73,500

(iii) a) Profit when actual sales drop by 10%
Sales = 18,50,000 – 10% = 16,65,000
Now, contribution at sales 16,65,000
16,65,000 × $$\frac{21}{100}$$ = 3,49,650
Profit = 3,49,650 – 3,15,000 = 34,650

b) Profit when actual sales increase by 5%
Sales = 18;50,000 + 5% = 19,42,500
Contribution at sales 19,42,500
19,42,500 × $$\frac{21}{100}$$ = 4,07,925
Profit = 4,07,925 – 3,15,000 = ₹ 92,925

Question 6.
A retail dealer in a garment is currently selling 24,000 shirts annually. He supplies the following details for the year ended 31 December 2010.
Selling price per shirt ₹ 400
Variable cost per shirt ₹ 250
Fixed Cost:
a) Salaries for the year — ₹ 12,00,000
b) General office costs for the year — ₹ 8,00,000
c) Advertising cost for the year — ₹ 4,00,000
From the above details:
a) Calculate break-even point and margin of safety in sales revenue and number of shirts sold.
b) Assume that 20,000 shirts were sold in a year and find out the net profit of the firm.
c) If it is decided to introduce, selling commission of ₹ 30 per shirt, how many shirts would require to be sold in a year to earn a net income of ₹ 1,50,000?
d) Assuming that for the year 2011, an additional staff cost of ₹ 3,30,000 is anticipated and price of a shirt is likely to be increased by 15%, what should be break-even point in number of shirts and sales volume?

Cost Control and Cost Reduction Questions and Answers

Question 1.
What is cost control?
Cost control is a series of steps that a business uses to maintain proper control over its costs. Implementing this level of control can have a profound positive impact on profits over the long term.

Question 2.
Define cost control.
CIMA, London has defined cost control as “the regulation by executive action of the cost of operating an undertaking particularly where action is guided by cost accounting”

Question 3.
What do you mean by cost reduction?
Cost Reduction is a process, aims at lowering the unit cost of a product manufactured or service rendered without affecting its quality by using new and improved methods and techniques. It ascertains substitute ways to reduce the cost of a unit. It ensures savings in per unit cost and maximization of profits of the organisation.

Question 4.
State the elements of cost reduction.
To identify cost reduction, the following are the major elements:

1. Savings in per unit cost.
2. No compromise with the quality of the product.
3. Savings are non-volatile in nature.

Question 5.
Define product design.
One area in which manufacturers are finding ways to meet this challenge is the oftenoverlooked area of product design. The design of the product provides the greatest scope for cost reduction.

Question 6.
What is Target costing?
Target costing is a system under which a company plans in advance for the product price points, product costs, and margins that it wants to achieve. If it cannot manufacture a product at these planned levels, then it cancels the product entirely.

Question 7.
What do you mean by value analysis?
Value: Analysis can be defined as, a process of systematic review that is applied to existing product designs in order to compare the function of the product required by a customer to meet their requirements at the lowest cost consistent with the specified performance and reliability needed.

Question 8.
What is Life Cycle Costing?
Life cycle costing estimates and accumulates costs over a product’s entire life cycle in order to determine whether the profits earned during the manufacturing phase will cover the costs incurred during the pre-and-post manufacturing stage.

Question 9.
What is Kaizen Costing?
Kaizen costing is the process of cost reduction during the manufacturing phase of an existing product. The Japanese word ‘Kaizen’ refers to continual and gradual improvement through small activities, rather than large or radical improvement through innovation or large investment technology

Question 10.
What is value engineering?
Value engineering (VE) is a systematic method to improve the “value” of goods or products and services by using an examination of function. Value engineering is also referred to as “value management” or “value methodology” (VM), and “value analysis” (VA). Value, as’ defined, is the ratio of function to cost. That is:
Value = $$\frac{\text { Function }}{\text { Cost }}$$

Question 11.
Give the meaning of value chain analysis.
Value chain analysis is a means of achieving higher customer satisfaction and managing costs more effectively. The value chain is the linked set of value creating activities all the way from basic raw materials’ sources, component suppliers, to the ultimate enduse product or service delivered to the customer.

Question 12.
What do you mean by Bench Marketing?
Bench marketing is a continual search for the most effective method of accomplishing a task by comparing the existing methods and performance levels with those of other. organizations or other sub-units within the same organization.

Question 13.
Give the meaning of business process re-engineering.
Business process reengineering (BPR) is the analysis and redesign of workflows within and between enterprises in order to optimize end-to-end processes and automate non-valueadded tasks.

Question 1.
Distuss the various steps in cost control
1. Establishing norms: The first step in cost control is to set norms or standards which may serve as yardsticks for measuring performance. These standards are set on the basis of past performance adjusted for changes in future and on the basis of studies conducted.

2. Comparison with actual: The actual cost incurred is compared with established standard costs to know the level of achievement. The variations are analyzed so as toy arrive at the causes which are controllable.

3. Corrective Action: Remedial measures are taken to avoid the recurrence of variation in future and for revision of standards wherever necessary steps in Cost control.

Question 2.
What are the essentials for success of cost control?
The essentials of success of cost control are:
1. Suitable: The control system should be appropriate to the nature and needs of the activity. A large firm calls for controls different from those needed for a small firm.

2. Timely and Forward Looking: The control system should be such as to enable the subordinates to inform their superiors expeditiously about the deviations and failures. The feedback system should be as short and quick as possible.

3. Objective and comprehensive: The control system should be both, objective and understandable. Objective controls specify the expected results in clear and definite terms and leave little room for argument by the employees.

4. Flexible: The control system should be flexible so that it can be adjusted to suit the needs of any change in the environment. A sound control system will remain workable even when the plans change or fail outright.

5. Economical: Economy is another requirement of every control. The benefit derived from a control system should be more than the cost involved in implementing it. A small company cannot afford the elaborate control system used by a large company.

6. Motivate People to High Performance: A control system is most effective when : it motivates people to high performance. Since most people respond to a challenge, successfully meeting to tough standard may well provide a greater sense of accomplishment than meeting an easy standard.

7. Corrective Action: In the words of Koontz and O’Donnell, “An adequate control system should disclose where failureis occurring, who is responsible for them and what should be done about them.” A control system will be of little use unless it can generate the solution to the problem responsible for deviation from standards.

8. Reflection of Organisation Pattern: Organization is not merely a structure of duties and function, it is also an important vehicle of control. In enforcing control the efficiency and the effectiveness of the organisation must be clearly brought out.

Question 3.
Discuss the various foois used for cost induction.
There are various tools used for cost reduction. Some of them are listed below:

a) Budgets, standard costing and variance analysis: Establishment of standards or limiting incurring of costs through budgets is the most common form of cost control and cost reduction exercise. A predetermined level of cost would force people in an organization to be cost conscious a look area to save or reduce cost. Some organization even encourage Cost Management cost cutting exercise by making saved cost as 50% distributable as incentive. Sometime back a state owned transport department organized what is called as “fuel saving week” to reduce consumption of diesel. At the entrance of each depot the amount of diesel so far used along with diesel consumed during the same period in the previous year was displayed. Such exercise creates awareness and seriousness among the staff and workers but also the general public. The goal appears half achieved.

b) Standardization and simplification: Methods of working if simplified and standardized would save cost to a very great extent. Re-working, duplication, un-necessary machine time, exposure to extra time that merited all bring about reduction in costs. Multitasking; concurrent operations are few examples for saving machine time and labour costs. Standardization and simplification of work methods and procedures not only reduces wastages they are particularly cost saving areas in the case of apprentice and trainees.

c) Quality control: Cost reduction or cost savings are not at the cost of quality Keeping the quality in-tact and at the same time, achieving savings in cost is the objective. The department endowed with quality assurance must view not only from adherence to preset :- standards of quality but also go an extra mile to find out the ways and means by which the same level of quality be ensured at reduced costs.

d) Work study: What are the various aspects that go into a particular task or work and the same is expressed in financial terms through estimated costs for each task or work. Then observation are made regarding the time, the materials used, the costs incurred, the various activities that are undertaken and an examination is made to discover whether there is scope for performing the same work with lesser materials, fewer interval of time, through minor changes in working postures etc. is undertaken from the perspective of savings in time, cost etc.

e) Job Evaluation and Merit Rating: The right time to achieve right cost. If there is a man-machine mismatch, it leads to incurring extra costs on all counts namely; materials, labour and overheads. The right match can be ensured through Job evaluation and through Merit Rating.

f) Production planning and control: Job sequencing and avoiding back-tracking of materials in production process reduces costs. Normally the whole production process is : a well thought and a well-knit plan. But with change in technology and minor change in work procedures are likely to enhance quality of job as also reduction in costs. Whenever: organizations are talking of multi-tasking and concurrent work processes, it is natural’ to give importance to production planning and control mechanisms from cost savings angle.

Question 4.
Explain the various techniques of Cost Reduction.
1. Just-In-Time (JIT) System: The main. aim of JIT is to produce the required items, at the required quality and quantity, at the precise time they are required. JIT purchasing requires for the items where too much carrying costs associated with holding high inventory levels. Purchasing system reduces the investment in inventories because of frequent order of small quantities.

2. Target Costing: Target costing refers to the design of product, and the processes used to produce it, so that ultimately the product can be manufactured at a cost that will enable the firm to make profit when the product is sold at an estimated market-driven price. This estimated price is called target price.

3. Activity Based Management (ABM): Activity based management is the use of activity based costing to improve operations and to eliminate non-value added cost. The main goal of ABM is to identify and eliminate non-value added activities and costs.

4. Life Cycle Costing: Life cycle costing estimates and accumulates costs over a product’s entire life cycle in order to determine whether the profits earned during the manufacturing phase will cover the costs incurred during the pre-and-post manufacturing stage.

5. Kaizen Costing: Kaizen costing is the process of cost reduction during the manufacturing phase of an existing product. The Japanese word ‘Kaizen’ refers to continual and gradual improvement through small activities, rather than large or radical improvement through innovation or large investment technology.

6. Business Process-re-engineering: Re-engineering is a complete redesign of process with an emphasis on finding creative new ways to accomplish an objective. The aim of business process re-engineering is to improve the key business process in an organization by focusing on simplification, cost reduction, improved quality and enhanced customer satisfaction.

Question 5.
Distinguish between cost control and cost reduction.
Difference between Cost control and cost reduction are:

 Cost control Cost reduction 1. Cost control is the achievement of pre- determined targets of costs 1. Cost reduction is the achievement of the real and permanent reduction in costs. 2. Cost control tends to assume a static state of affairs and that standard once set are not challenged. 2. Cost reduction assumes the existence of concealed potential saving in the standards or pre- determined costs set for cost control and that these standards are always subject to challenge. 3. Cost control is concerned with predetermining costs, comparing it with actual costs, analysing the variances and taking corrective, measures. 3. Cost control is concerned with predetermining costs, comparing it with actual costs, analysing the variances and taking corrective measures. 4. Cost control is concerned with predetermining costs, comparing it with actual costs, analysing the variances and taking corrective measures. 4. Cost reduction is not concerned with: maintenance of performance according to predetermined targets. it is rather concerned with finding out new product design, methods, etc 5. Cost control, is a part of cost accounting function. 5. Cost reduction may be achieved even when no cost accounting system is in operation. 6. Cost control lacks dynamic approach to cost improvement 6. Cost reduction is more dynamic approach to cost improvement.

Question 6.
Discuss the areas covered by cost control and cost Reduction.
1. Product Design: One area in which manufacturers are finding ways to meet this challenge is the often-overlooked area of product design. The design of the product provides the greatest scope for cost reduction. There are two basic points that need to be remembered while effecting cost reduction in product design:

1. the product should perform all the functions for which it was intended.
2. the product should retain its esteem or aesthetic value.

Improvement in product design may result in cost reduction as illustrated below:
(a) Material Cost: Change in design of the product may result in saving the material cost. Economical substitution for existing material may also be considered. Example: in manufacturing kitchen utensils, brass may be substituted with cheaper alloys.”
(b) Labor cost: Improvement in design may result in reduced operating time.
(d) Packing and transporting: Compact design will reduce cost.

2. Organisation: Cost reduction may also be achieved by improving factory organisation in the form of clear-cut lines of authority and responsibility, well-defined channels of communication, co-ordination and co-operation conductive to efficiency.

3. Production: A cost reduction programme should make a study of sequence of operations to find out the best one, to use the most suitable machines for the work, to use jigs and fixtures to reduce operating time, to reduce idle time, to reduce scrap by the use of better quality tools, to provide better working conditions conductive to efficiency.

4. Administration: An organisation should make efforts to reduce the cost of administrative expenses, as there is ample scope to do so. A company may evaluate and reduce the cost of following expenses, but not the cost of efficiency: Modifying range of discounts Modifying internal and external communication Telephone expenses Travelling expenses Salary by reducing staff Reduction in cost of stationery,

5. Marketing: In this function, costs can be reduced by revising the methods of remuneration of salesmen, re- arrange territorial responsibilities of sales representatives, modifying current methods of advertising, improving product design and production quality so as to reduce after sales service, economising channels of distribution, improving packing etc.

6. Finance: Finance is an important area where cost reduction is possible through the following measures:

1. Control over utilization of finance meant for both working capital and fixed capital needs.
2. Proper evaluation of investments in new projects.
3. Appropriate control of capital expenditure.
4. Profitable employment of capital with the objective of maximum return.

Question 7.
Discuss the approaches to Target costing as a means to cost Reduction.
The design team uses one of the following approaches to more tightly focus its cost reduction efforts:
a) Tied to components. The design team allocates the cost reduction goal among the various product components. This approach tends to result in incremental cost reductions to the same components that were used in the last iteration of the product. This approach is commonly used when a company is simply trying to refresh an existing product with a new version, and wants to retain the same underlying product structure. The cost reductions. achieved through this approach tend to be relatively low, but also result in a high rate of product success, as well as a fairly short design period.

b) Tied to features. The product team allocates the cost reduction goal among various product features, which focuses attention away from any product designs that may have been inherited from the preceding model. This approach tends to achieve more radical cost reductions (and design changes), but also requires more time to design, and also runs a greater risk of product failure or at least greater warranty costs.

In these methods, companies are more likely to use the first approach if they are looking for a routine upgrade to an existing product, and the second approach if they want to achieve a significant cost reduction or break away from the existing design. ::

Question 8.
What are the characteristics of target costing?
1. Target costing is used in the planning and design stages.
2. Target costing is a tool for cost reduction, Conceptually, cost management can be divided into two parts: cost reduction and cost control. Target costing is clearly focused on cost reduction.
3. Target costing is a market-driven technique.

4. Target costing is usually part of strategic profit planning for multiple years. In fact, target costing is often used as a bottom-up tool for attaining the profit goal set by top management when it determines middle-range corporate strategy.

5. Target costing is an engineering-oriented technique.

6. Target costing is a management tool for directing and focusing the decision process for design specifications and production engineering.

Question 9.
Explain the principles of target costing.
a) Principles of Price-led costing: Under this principle the market prices are used to determine the target costs. Target costs are calculated using a formula, market price required profit margin.

b) Principle of Focus on customers: The main features are customer requirements for quality, cost, and time are included in product and process decisions and guide cost analysis. The value must be greater than the cost of providing those features and functionality.

c) Principles of Focus on Design: The cost control at this phase is emphasized at the product and process design stage. This results in lower costs and reduced “time-to: market” for new products.

d) Cross-functional involvement Principles. The main involvement is done by the cross-functional product and process teams who are responsible for the entire product from initial concept through final production.

e) Value-chain involvement Principle: The value chain enablers i.e. the suppliers, distributors, service providers, and customers are involved in the process.

f) A life-cycle orientation Principle: Total life-cycle costs which include purchase price, operating costs, maintenance, and distribution costs are minimized for both the producer and the customer.

Question 10.
What are the advantages of target costing?
1. Making possible equitable and scientific pricing by reducing prices of products that useless activity resources and increase prices of products that consume more of the firm’s activity resources.
2 Helping organizations provide value added services or “top-ups” to existing products on actual cost incurred basis.

3. Eliminating unprofitable items from the product line, thereby increasing profitability without increasing prices, a valuable option in recessionary times.

4. Eliminating the cost of maintaining or running non-remunerative activities, increasing overall profitability.

5. Allowing allocation of resources to profitable items or items that use fewer resources.

6. Ensuring compatibility with performance management scorecards by revealing per person contribution to the product cost, and hence, profits.

7. Exposing waste and inefficiency that contributes to boosting productivity.

Question 11.
What are the disadvantages of target costing?
1. In the anxiety to contain costs within target, essential costs may be omitted or compromised leading to loss.

2. The working accuracy of the target cost is very difficult. It presupposes that people in the organization are well aware of the various cost structure and margin up to which they may continue to incur costs. This may not be totally true in all cases. There is an eminent danger.

3. The cost incurred may be different leading to under or over costing, unless there is a mechanism to collect actual costs and compare them with targets. There is a need for a mechanism to monitor costs. This is practically not possible.

Question 12.
What are the objectives of value analysis?
1. To provide better value to a product/service.
2. To improve the company’s competitive position.
3. To ensure that every element of Cost contribute equally to the function of the product.
4. To eliminate unnecessary Cost.

Question 13.
What are the applications of value analysis?
1. Capital goods – plant, equipment, machinery, tools, etc.
2. Raw and semi-processed material, including fuel.
3. Materials handling and transportation costs.
4. Purchased parts, components, sub-assemblies, etc.
5. Maintenance, repairs, and operational items.
6. Finishing items such as paints, oils, varnishes, etc.
7. Packing materials and packaging… 8. Printing and Stationery items.
9. Miscellaneous items of regular consumptions.
10. Power, water supply, air, steam and other utilities

Question 14.
Explain the importance of Business process re-engineering.
Business process re-engineering is a business management strategy, originally pioneered in the early 1990s, focusing on the analysis and design of workflows and processes within an organization. BPR aimed to help organizations fundamentally rethink how they do their work in order to dramatically cut operational costs, improve customer service and become world-class competitors. In the mid-1990s, as many as 60% of the Fortune 500 companies claimed to either have initiated reengineering efforts, or to have plans to do so.

BPR seeks to help companies radically restructure their organizations by focusing on the ground-up design of their business processes. According to Davenport a business process is a set of logically related tasks performed to achieve a defined business outcome. Reengineering emphasized a holistic focus on business objectives and how processes related to them, encouraging full-scale recreation of processes rather than iterative optimization of sub processes. These activities aim at improving performance through work analysis, design, re-design of workflows and processes within an organization. The undertaking of this exercise coupled with cost savings angle is the need of the hour. This is so because the whole process is undertaken by comparing production activities with the world’s greatest manufacturing units.

Assessment of Companies Questions and Answers

Question 1.
Give the meaning of Company.
According to Section 2 (17) Company means any Indian Company or any body corporate incorporated under the law of a foreign country or any institution, association or body which was assessable or was assessed as a company for any assessment year upto 1970-71 or any institution, association or body whether incorporated or not whether Indian or non-Indian, which is declared by general or special order of CBDT to be company.

Question 2.
Give the meaning domestic Company.
It means an Indian Company or any other company which in respect of its income liable to pay tax under the Act in accordance with Section 194.

Question 3.
Explain residential Status of a company- Section 6(3).
A Company is said to be a resident if it is an Indian Company. If the control & management of the company is wholly situated in India it is said to be a resident. If the control & management of its business affairs is partly or wholly situated outside India, it is said to be a non-resident under section 2(30) of the Income Tax Act of 1961. Thus a company enjoys two status, resident & non-resident.

Question 4.
State different types of company.
The different types of companies are

1. Domestic company.
2. Foreign company.
3. Public company.
4. Private company.

Question 5.
What do you mean by domestic company?
A Domestic Company means an Indian Company or any other company with respect to its income, liable to pay tax under the Income-Tax Act, has made the prescribed arrangements for the declaration and payment within India, of the dividends (including dividends on preference shares) payable out of such income.

Question 6.
What do you mean by foreign company?
Foreign company means a company registered outside India in any other foreign country.

Question 7.
What do you mean by public company?
Public company means a company which is not a private company.

Question 8.
What do you mean by private company?
Private company means a company which, by its articles, restricts the right to transfer its shares, if any; limits the number of its members to fifty not including persons who are in the employment of the company.

Question 9.
What is zero tax companies?
The companies who had book profits as per P&L A/C but the total income as per provisions of the income tax act either nil/negative such companies were not paying any income tax. Such companies called Zero Tax Companies.

Question 10.
How do you computation of Total Income?
First the taxable income under each head of income after deducting expenses & losses. The total of the balances in each head is known as Gross Total Income. The deductions are allowed Under Section 80G, BOGGA, 80GGB,
80-IA, 80-IB, 80-IAB, 80-IC, 80-ID, 80-IE, 80JJA, 8OJJAA & 80LA. The balance amount is taxable total income.

Question 11.
Expand PFAAS and AOP.
PFAAS – Partnership Firm Assessed as such
AOP – Association of Person.

Question 12.
Explain assessment of Companies.
A Company is required to file its return of income under section 139(1) of the Income Tax Act of 1961 within a prescribed time. The due date for filing the return of income by a company is 30th September of the assessment year. A Company is liable to pay income tax on its total income, however small it may be.

Question 13.
What is widely held company?
2016 A company in which the public are substantially interested is known as widely held company.

Question 14.
Define depreciation.
Depreciation is a charge on assets used for generating income during the previous year.

Question 15.
It is an extra depreciation allowable at 20% together with normal depreciation on new machinery purchased during the relevant previous year. It is allowed only in the year in which machinery is purchased and in the subsequent years no additional depreciation can be claimed.

Question 16.
What is MAT?
Minimum alternate tax ensures that no taxpayer with substantial income can avoid tax liability by using exclusions, deduction and incentives.

Question 17.
What is tax credit under MAT?
If the amount of tax payable by the company under MAT is more than the amount of tax payable at normal rate the difference is known as tax credit. The amount of tax credit can be recovered in the next ten years out of the excess amount of tax payable by the company at normal rate.

Question 1.
Explain different types of companies.
The different types of companies are as follows:
1. A Domestic Company means an Indian Company or any other company with respect to its income, liable to tax under the Income Tax Act, has made the prescribed arrangements for the declaration and payment within India, of the dividends (including dividends on preference shares) payable out of such income.

2. Foreign company means a company registered outside India in any other foreign country.

3. Public company means a company which is not a private company.

4. Private company means a company which, by its articles, restricts the right to transfer its shares, if any; limits the number of its members to fifty not including persons who are in the employment of the company.

Question 2.
Explain computation of depreciation.
As per income tax depreciation is calculated on Written down value method (WDV). In the case asset is acquired during the year, actual cost of asset will become WDV. for calculation. In the case asset is acquired before previous year, the WDV will be actual cost to the assessee less the aggregate of all the depreciation actually allowed as deduction in respect of depreciation. If there is any unabsorbed depreciation, the same will considered as deemed depreciation actually allowed. Net block-(WDV on which depreciation will be calculated)
(In above calculation if asset is used for less than 180 days, WDV less purchased asset eligible for half rate= full rate and remaining will be depreciated by half rate).

Question 3.
Discuss the computation of taxable income of the companies.
1. Ascertain the ‘total income’ of the company by aggregating incomes falling under following four heads
a) Income from House Property, whether residential or commercial, let-out or selfoccupied. However, house property used for purpose of company’s business does not fall under this head.
b) Profits and Gains of Business or Profession.
c) Capital Gains.
d) Income from other sources including interest on securities, winnings from lotteries, races, puzzles, etc.

2. To the total income so obtained, ‘current and brought forward losses’ should be adjusted for set off in subsequent assessment years to arrive at the gross total Income.

3. From the gross total income, prescribed ‘deductions’ under Chapter VI A are made to get the net income.

4. Tax liability is computed on the ‘net income’ that is chargeable to tax. It is done either on accrual basis or on receipt basis.

Question 4.
Explain the rates of Income Tax for A.Y.2018-19.
In case of a domestic company:

1. Winning U/S 115BB-30%
2. Short term capital gain U/S 111A-15%
3. Long term capital gain U/S 112-10%/20%
4. Other income-30%

Surcharge at 5% on the amount of income tax, if total income exceeds one crore rupees. Health and Education Cess is at 4%.
In case of company other than a domestic company:
1. Income from royalty received from government or an Indian concern before 1st April 1976- 50%
2. Income from fees for rendering technical services received from Government or Indian concern before 1st April 1976- 50%
3. Winning U/S 115BB-30%
4. Short term capital gain U/S 111A-15%
5. Long term capital gain U/S 112- 10% / 20% .
6. Other income- 40%

Surcharge @ 2% on the amount of income-tax, if total income exceeds one crore rupees. Health and Education Cess @ 4% is charged.

Question 5.
Briefly explain MAT.
Minimum Alternative Tax (MAT) U/S 115JB
Where in the case of a company the income tax payable on its total income in respect of any previous year relevant to assessment year on or after 1-4-2012 is less than 18.5% (Plus surcharge, if any + Health and Education Cess) of such book profit. The surcharge of domestic company is 5% if total income or book profit exceeds one crore rupees and in case of foreign company 2%, if total income or book profit exceeds one crore rupees. The Health and Education Cess is @ 4%.

Thus the Minimum tax on Book Profit will be 18.5% plus Surcharge 5% if book profit exceeds one crore rupees plus education cess @ 3%.
Company in which the Public are substantially interested-Section 2(18)

1. Owned by Government/RBI-Holds more than 40% of shares.
2. Companies U/S 25-Promotion of art, science, commerce, charity.
3. Company without share capital.
4. Nidhi/ Mutual benefit society.
5. Company owned by co-operative society.
6. Listed Company
7. Public limited company owned by government or widely (50%) held company.

Question 6.
Write a short note on MAT-Sec 115JB.
The concept of Minimum Alternate Tax (MAT) was introduced in the direct tax system to make sure that companies having large profits and declaring substantial dividends to shareholders but who were not contributing to the Govt by way of corporate tax, by taking advantage of the various incentives and exemptions provided in the Income-tax ‘Act, pay a fixed percentage of book profit as minimum alternate tax.

Section 115JB, inserted by the Finance Act, 2000 has cast a responsibility on the Chartered accountant to certify that the book profit has been computed in accordance with the provisions of the Income-tax Act. He has also to certify the income-tax payable by the company.

The provisions of MAT can be clearly understood with the help of following example:
1. Every company required to compute tax both under the income tax and under sec 115 JB

2. Profit computed under the income tax is called regular profit and the tax under this method is called regular tax

3. Profit computed under sec 115JB is called Book profit and the tax computed is called MAT.

4. Every year a company required to compute the tax under the both methods and required to pay higher of those.

5. The company which has paid the MAT in any year can carry forward to the next subsequent years to setoff against the tax liability in which it pays the regular tax.

6. However a company is not required to compute its book profit and pay the MAT in the in year in which it has its regular profit itself “nil” or “loss”

MAT Credit to the extent of the MAT paid excess of the regular tax can be taken as credit and can be carry forward to the next subsequent years.

MAT Credit Utilisation Lower of the following is available for utilization of the credit

1. MAT credit
2. The extent of the higher of the regular tax paid over and above MAT

Practical Problems

Question 1.
State whether the following are admissible or inadmissible expenses under o the provisions of Income Tax Act.
1) A cash payment of ₹ 18,500 paid to a supplier of raw materials on a day, on which the banks were closed on account of in-definite strike.
2) Depreciation of ₹ 40,000 is debited to P and L A/c on Sri Ram Temple which is constructed. inside the factory premises for the benefits of employees of the company.
3) Contribution made by company to Staff Welfare Fund.
4) Donation to NCF ₹ 25,000
5) Bonus of ₹ 75,000 was paid to the employee after the due date of filing return of income
6) Service tax paid
7) Provision for income tax
8) Of the sales tax provision sales take of ₹ 10,000 was paid before filing the return of income.

Question 2.
A block of asset consist of 5 machines. The WDV of machinery as on 1.4.2017 is ₹ 1,80,000. Rate of depreciation is 15%.
A new machine costing ₹ 1,60,000 was acquired in May 2018 but actually put to use only on 10.10.2017.
Two old machines are also sold for ₹ 3,20,000 in December 2018.
Determine amount of depreciation for the A.Y. 2019-20.

Question 3.
The book profit of the company is ₹ 3,00,000. Compute its tax liability.

Question 4.
Sharada Ltd., is engaged in the business of manufacture of refrigerators since 1998.
The following assets are acquired during 2018-19: Date of acquisition and being put into use Aug. 2018 June 2019 Jan2012
Find out the following:
b) Depreciated value of the blocks on April, 2018.

Question 5.
Rising Sun Co. Ltd. is engaged in the business of manufacture of computer components.
The profit and loss A/c of the company for the year ending 31.3.2019 is given below:  Other information:
1) Depreciation allowable as per IT rules works out to ₹ 1,45,000
2) Brought forward business loss ₹ 3,50,000
3) Brought forward unabsorbed depreciation ₹ 1,45,000
4) of the custom duty payable ₹ 12,000 was paid before filing the return
Company is eligible for following deductions:
Deduction U/S 80 IB (25% of ₹ 28,50,000)
Deduction U/S 80G in respect of Donation to NDF.
Calculate the total income of Rising Sun Co. Ltd., and tax liability for the assessment year. 2019-20.

Question 6.
Compute Total Income of M/S Anandi Company Limited for the Assement Year 2019-20.
1. Income from leather business ₹ 80,000.
2. Interest for deferred payment of octroi duty ₹ 2,000.
(Business income computed before charging this)
3. Dividend from Indian Company (Gross). ₹ 25,000.
4. Collection Charges of Dividend ₹ 3,000.
5. Brought forward business loss from previous year ₹ 80,000.

Question 7.
The total income of a company is 5,78,000 out of which Long Term Capital Gain is ₹ 33,000 and Income from Business is 5,45,000. The Book Profits of the company is ₹ 10,00,000.

Question 8.
The total income under the Income Tax Act of 1961 is ₹ 4,50,000.
The Book Profits of a company in the previous year 2018-19 in view with U/ S 115JB of the Income Tax Act is ₹ 15,00,000. Is the Company liable to pay MAT? If yes how much has to be paid.

Question 9.
The Gross Total Income of M/S SNS Ltd was computed for the A.Y.2019 2020 as follows:
1. Income from Rice Mill ₹ 1,50,000.
2. Income from Steel Company ₹ 1,90,000.
3. Profit of new industrial unit situated in Backward Industrial State which was established in 2012 ₹ 85,000
4. Income from Poultry Farming which was started in November 2012 ₹ 1,00,000..
5. Short term capital loss ₹ 60,000.
6. Income from Royalty from Indian Company ₹ 75,000.
7. Dividend from a domestic company ₹ 50,000.
8. Long term capital gain ₹ 1,00,000.
9. Export Business Profit ₹ 3,00,000.
The Company donated ₹ 50,000 to Chief Minister’s Drought Relief Fund. Compute Taxable Total Income.

Question 10.
M/S Sheela Company Limited is a domestic company. The following incomes B are furnished by the company:
a) Income from Export Business ₹ 1,25,00,000.
b) Dividend from Foreign Company ₹ 1,00,000.
c) Dividend from Domestic Company (Net) ₹ 50,000.
d) Long term capital gain ₹ 2,00,000.
e) Short term capital gain ₹ 1,25,000.
f) Income from Listed Securities (Gross) ₹ 75,000.
g) Income from Post Office Savings Bank Account ₹ 1,00,000.
h) Book Profit Under Section 115JB ₹ 90,00,000
The Company donated ₹ 1,00,000 towards Prime Ministers Flood Relief Fund. Compute the total taxable income & tax liability for the A.Y. 2019-20.

Question 11.
Nirmala Roy Traders Limited closes its accounts on 31st March every year, For the year 2018-19 the following details are given:
a) Income from royalty from a foreign company ₹ 32,00,000.
b) Income from units of UTI Rs 10,000
c) Dividend from a Co-operative Society ₹ 50,000
d) Dividend from a Domestic Company ₹ 30,000
e) Dividend from Foreign Company ₹ 1,50,000
f) Rent from House Property ₹ 50,000
g) Municipal tax paid on House Property ₹ 5,000
h) Long term capital gain ₹ 1,00,000
i) Short term capital loss ₹ 40,000
j) Income from business (computed) ₹ 3,00,000
The business was started in the backward state in 2005-2006.
Donation to PM Relief Fund ₹ 1,00,000.
Compute Taxable Total Income for the A.Y.2019-20.

Assessment of Firms Questions and Answers

Question 1.
What is partnership?
Partnership is, “relationship between persons who have agreed to share the profits of a business carried on by all or any of them acting for all”

Question 2.
What is partnership deed?
It is a legal document which contains the agreement between partners in respect of sharing of profits or losses, capital contributions, interest on capital and drawings, remuneration payable to partners and rights and duties of partners etc.

Question 3.
What is firm?
Firm is defined in Section 2(23) of the income tax act, 1961 as follows: Firm shall have the meaning assigned to it in the Indian Partnership act, 1932 and shall include a limited liability partnership as defined in the limited liability Partnership Act, 2008.

Question 4.
Who is a partner?
“Partner” shall have the meaning assigned to it in the Indian Partnership Act, 1932 (9 of 1932), and shall include:
(a) Any person who, being a minor, has been admitted to the benefits of partnership and
(b) A partner of a limited liability partnership13 as defined in the Limited Liability Partnership Act, 2008 (6 of 2009).

Question 5.
Mention any two features of partnership firm.
The features of partnership are:

1. Agreement: The partnership arises out of an agreement between two or more persons.
2. Profit sharing: There should be an agreement among the partners to share the profits of the business.
3. Lawful business: The business to be carried on by a partnership must always be lawful.

Question 6.
State different types of partners.
The different types of partners are as follows:

1. Limited partnership.
2. Limited liability companies.
3. Limited liability partnerships.

Question 7.
Who is working partner?
The partner who is aggressively occupied is conducting the affairs of the business or profession of a firm is called working partner.

Question 8.
Who is non-working partner?
The partner who is not aggressively occupied is conducting the affairs of the business or profession of a firm is called non-working partner.

Question 9.
Mention any two advantage of limited liability partnership.
It has separate legal entity, it has perpetual succession, the life of the firm is not depending on the life of its partners, the labilities of the partners’ is limited to the extent of agreed contribution in LLP, dissolution of partnership agreement will have no impact on the existence of LLP.

Question 10.
Define interest.
As per section 51(52(28A), interest means interest payable in any manner in respect of any moneys borrowed or debt incurred (including a deposit, claim or other similar right or obligation) and includes any service fee or other charge in respect of the moneys borrowed or debt incurred or in respect of any credit facility which has not been utilized.

Question 11.
What do you mean by capital?
Capital gains are existence of a capital asset, transfer of such capital asset and profits or gains that arise from such transfer.

Question 12.
Define salary.
Salary is defined as remuneration received by an individual for services rendered by him to undertake a contract whether it is expressed or implied.

Question 13.
Define commission.
As per section 194H commission includes any payment received or receivable by a person acting on behalf of another person for services rendered or for any services in the course of buying or selling of goods or in relation to any transaction relating to any asset, valuable article or thing, not being securities.

Question 14.
Give the meaning of book profit.
It means the net profit as per profit and loss account for the relevant previous year computed in accordance with sections 30. to 44D. The provisions of Section 40 (b) has to be complied while determining the book profit of the firm.

Question 15.
What will be “out of GST”?
Petroleum products.

Question 16.
State any three examples of disallowed expenses in case of firm.

1. Partnership deed expenses,
2. Personal expenses of partner,
3. Irrecoverable private hand Ioans.

Question 16.
List the deductions under Section 80 applicable to a firm.
U/s 80G, 80GGA, 80GGB, 801A, 801AB, 80IC, 80ID, 801E, 80JJA.

Question 1.
Discuss new scheme of taxation of firm.
The new scheme of taxation of firm includes:

1. Rate of tax.
2. Interest to Partners.
3. Remuneration to Partners.
4. Conditions for allowance of remuneration and interest to partners.
5. Conditions for assessment as a firm.
6. Partners’ assessments.
7. Losses of the firm.
8. Due dates for filing of returns of partners.

Question 2.
How to assessment of firm (Section 184)?
The assessment of firm (Section 184) is as follows:
1. A firm shall be assessed as a firm for the purposes of this Act, if

• The partnership is evidenced by an instrument and
•  The individual shares of the partners are specified in that instrument.

2. A certified copy of the instrument of partnership referred to in sub-section (1) shall accompany the return of income of the firm of the previous year relevant to the assessment year commencing on or after the 1st day of April, 1993 in respect of which assessment as a firm is first sought.

3. Where a firm is assessed as such for any assessment year, it shall be assessed ‘ in the same capacity for every subsequent year if there is no change in the constitution of the firm or the shares of the partners as evidenced by the instrument of partnership on the basis of which the assessment as a firm was first sought.

4. Where any such change had taken place in the previous year, the firm shall furnish a certified copy of the revised instrument of partnership along with the return of income for the assessment year relevant to such previous year and all the provisions of this section shall apply accordingly.

5. The “Profits and gains of business or profession” and such interest, salary, bonus, commission or remuneration shall not be chargeable to income-tax under clause (v) of section 28.

Question 3.
Discuss the treatment of interest and capital gains by partners to computation total income of firm.
Treatment of Interest
While computing taxable profits under the head ‘profits and gains of business or profession, a deduction is allowable to the firm on account of interest and remuneration payable to the partners. Deduction of interest to a partner is allowable u/s 36 and remuneration to a working partner will be allowed u/s 37. The deductions on account of interest and remuneration to the partners can be claimed under Sections 36 or 37

Capital Gains
Profits or gains arising from the transfer of a capital asset made in a previous year are taxable as capital gains under the head “Capital Gains”. The important ingredients for capital gains are, therefore, existence of a capital asset, transfer of such capital asset and profits or gains that arise from such transfer.

Question 4.
How do you treat various losses of Firm.
The Firm’s losses is treated in the following manner:
1) Speculation Losses can be set off against the Speculation Gain if any, otherwise it can be carried forward for four years ands written off.

2) Non-speculation Losses can be set off against any other income and can be carried. forward for eight years & written off.

3) Short term capital Losses can be set off against Short term capital gain or Long term capital gain.

4) Long term capital Losses can be set off only against Long term capital gain if any.

Question 5.
State whether the following are admissible or inadmissible expen ses under the provsions of Income Tax Act.
a) Discount Allowed.
b) Annual listing fees paid towards stock exchange by a company
c) LIC premium on director and his family members life.
d) Payment of licence fees for obtaining franchise.
e) Depreciation of ₹ 40,000 is debited to P/L A/c of Sri Ganesha Temple which was constructed inside the factory premises for the benefit of employees of the company.
f) Interest on loan taken to pay income tax.

Question 6.
State weather the following are admissible or inadmissible expenses under the provisions of Income Tax Act:
b) L.I.C. premium on Director and his family member’s life
c) Payment of licence fees for obtaining franchise
d) Professional Tax paid
e) Annual listing fees paid towards stock-exchange by a company
f) Expenditure paid
g) Pension paid to employees.
b) L.I.C. premium on Director and his family member’s life – Inadmissible
c) Payment of licence fees for obtaining franchise – Inadmissible
d) Professional Tax paid – Admissible
e) Annual listing fees paid towards stock-exchange by a company – Admissible
g) Pension paid to employees. – Admissible

Question 7.
State whether the following payments are admissible or not while calculating the business income under the provisions of Income Tax Act.
(i) Loss of stock due to theft by an employee
(ii) Service charged
(iii) Charities paid
(iv) Provisions for doubtful debt
(v) Legal expenses to defend on existing title to a capital asset.
(vi) Loss on sale of capital asset.
(i) Loss of stock due to theft by an employee – Admissible
(iv) Provisions for doubtful debt – Inadmissible
(v) Legal expenses to defend on existing title to a capital asset – Admissible
(vi) Loss on sale of capital asset – Inadmissible

Question 8.
Give the format of determining book profit.

Question 9.
Give the format computation of total income of a firm.

Question 10.
Veeresh and Co. had a block of plant and machinery having WDV of ₹ 50,00,000 as on 1-4-2018. During the year an additional machinery costing 20,00,000 was purchased on 5-9-2018.
On 2-11-2018 fire had broken in the premises of the company destroying a considerable part of the old plant and machinery. Insurance company paid the damages of ₹ 25,00,000. The rate of depreciation applicable is 10%.
Calculate the amount of depreciation chargeable to P and L a/c for the year ended 31-3-2019.
Will it make any difference if the entire block of plant and machinery is destroyed by fire? Show the calculations assuming that the claim amount ₹ 25,00,000 remain same.

Practical Problems

Question 1.
Sri Ram and Raghuram are working partners in a professional firm which satisfies all conditions of Sections 184 and 40(b) of IT Act.
They share profits and losses in the ration 4 : 1.
Profit and Loss A/c of the firm for the year ending 31.3.2019.
Compute the permissible amount of remuneration to partners.

Question 2.
Sheela, Nirmala & Sharmila are partners in a Firm sharing profits & losses in the ratio of 2:2:1 respectively.
The Profit & Loss Account for the year ended 31st March 2019 is as follows.
Compute the Total Income of the Firm & Taxable Income of the three partners in the Firm SNS. Nirmala and Sharmila are working partners.

Question 3.
Ram, Shyam & Sajib are partners of a firm with equal shares.
The profit & loss a/c for the year ended 31st March 2019 shows a net profit of ₹ 1,00,000 after debiting the following as per the Deed:
1. Salary to Ram ₹ 20,000 and to Shyam ₹ 15,000
2. Bonus to Sajib ₹ 15,000.
3. Interest on capital to Ram ₹ 2,000.
4. ₹ 20,000 paid for the rent of the business premises.
5. Commission of ₹ 5,000 was given to Sajib.
Compute Book Profit and the Total Income of the Firm assuming all the Partners are working partners.

Question 4.
P, Q & Rare partners in a firm assessed as firm sharing profits & losses equally.
The firm’s profit & loss account for the year ended 31st March 2019 showed a Net Profit of ₹ 2,00,000 after debiting the following:
1. Salary of ₹ 10,000 paid to R.
2. Commission to Q ₹ 5,000.
3. Donation to NDF ₹ 15,000.
The amount of Net Profit includes Rs 10,000 interest on Government Securities. All the partners are working partners.
Compute Firm’s Business Profits for the Assessment Year 2019-2020.

Question 5.
Compute the tax payable by AOP for the A.Y. 2019-20 if Smt. Anandi a member is liable to pay tax on his income.
Following is the list of
Income from House Property (Computed) ₹ 40,000.
1. Winning from Karnataka State Lottery (Gross) ₹ 50,000.
2. Income from Long Term Capital Gain ₹25000.

Question 6.
Calculate allowable remuneration to the working partners.
Net profit as per P/L A/c ₹ 1,35,000 after debiting the following items:

 ₹ Salary to partners 1,25,000 Commission to partners 1,00,000 Bonus to partners 25,000

Question 7.
The AOP who furnishes the following incomes for the A.Y. 2019-20 are given below:
Long term capital gain ₹ 12,000
Income from House Property ₹ 1,81,000.

Question 8.
Compute the total income of a firm for the Assessment Year 2018-19.
a) Profit from a garment industry ₹ 5,50,000.
b) Profit from small scale industrial undertaking established in backward state in March 2019 ₹ 2,00,000.
c) Long term capital gain ₹ 4,00,000.
d) Short term capital loss ₹ 2,00,000.
e) Interest from Non-Government Securities (Gross) ₹ 50,000.

Question 9.
The total income of a firm is 66,500 and the long term capital gain is ₹ 4,00,000
Compute the tax payable by the firm.

Question 10.
X,Y & Z are the partners in a firm of which X and Y are working partners.
Net profit as shown by P&L A/c is ₹ 90,000 after debiting the following:
a) Interest on Capital at 18%

 X ₹ 9,000 Y ₹ 12,000 Z ₹ 6,000

b)

 X ₹ 1,00,000 Y ₹ 1,10,000

Calculation of income from professional firm:

Question 11.
X,Y and Z are the partners in a firm sharing profits and losses in the ratio of 3:2:1.
The total income of the includes the following:
Income from business of firm ₹ 3,50,000
Income from house property ₹ 50,000
Short-term capital gains u/s111A ₹ 40,000.
Long-term capital gains u/s112 ₹ 60,000
Compute the tax liability of firm for the assessment year 2019-20.

Question 12.
A, B and C are the partners sharing profits and losses equally in a firm.
During the year 2018-19 the firm incurs a net loss of 36,00,000 after deducting the following:
(a) Commission to ₹ 40,000
(b) Bonus to B and ₹ 780,000 each
(c) Salary to A, B and C ₹ 160000 each
(d) Donation to PM’s National Relief Fund ₹ 80,000
(e) Income Tax ₹ 40,000
(f) Sales Tax ₹ 1,00,000
(g) Office rent ₹ 1,00,000
(h) Depreciation on assets 1400000 (Allowable depreciation as per IT law is ₹ 4,80,000)
(i) Interest on Capital Calculated at 20%
A – ₹ 64,000
B – ₹ 56,000
C – ₹ 72,000
The profit and loss a/c also included the following incomes
(i) Long term Capital gain ₹ 90,000
(ii) Short term Capital gain ₹ 70,000
(iii) Export earnings ₹ 3,80,000
Compute the book profit of the firm for the A.Y. 2019-20.

Tax Under E-Environment Questions and Answers

Question 1.
What is return of income?
A return of income is a defined form which can list out the particulars of income and the taxes paid on the same by an individual, firm or organisation in a financial year. This in turn can be presented to the Income Tax Department.

Question 2.
What is defective returns.
Defective returns are chose income tax returns that are deemed to contain specific defects as outlined in the provisions of Section 139(9).

Question 3.
What is E-Filing?
E-filing or electronic filing is submitting the income tax returns online. There are two ways to file the income tax returns. The traditional way is the offline way, where assessee go the Income Tax Department’s office to physically file the returns.

Question 4.
Expand PAN.
PAN: Permanent Account Number

Question 5.
Give the meaning of PAN.
Permanent Account Number is a ten-digit alphanumeric number issued in the form of laminated card by the Income Tax Department to any “person” who applies for it or to whom the department allots the number without an application.

Question 6.
What do you mean by digital signature.
Digital signature is a technical term, defining the result of a cryptographic process that can be used to authenticate a sequence of data.

Question 7.
Give the meaning of digital certificate.
A digital certificate is an electronic document issued by a Certificate Authority. It contains the public key for a digital signature and specifies the identity associated with the key, such as the name of an organization.

Question 8.
Expand PKI.
PKI: Public Key Infrastructure.

Question 9.
What is TDS?
TDS or Tax Deducted at Source at prescribed rates is made mandatory by the Income Tax Act on certain persons responsible for making payments. The tax deducted has to be deposited by them to the government. The recipient of income receives the net amount

Question 10.
What is advance payment of tax.
Advance tax is applicable when an individual has sources of income other than his/ her salary. For instance, if one is earning through capital gains, interest on investments, lottery, house property or business, the concept becomes relevant.

Question 1.
State the different types of income tax returns.
1. Mandatory Return and Voluntary Return Section 139(1)
2. Return of Loss Section 139(3) 3. Belated or Late Return of Income Section 139(4)
4. Revised Return Section 139(5)
5. Return of Income of a Charity or Religious Institution Section 139(4A)
6. Return of Income of a Political Party Section 139(4B)
7. Section 139(40) and Section 139(4D)
8. Defective Returns Section 139(9)

Question 2.
What are the due date for filing returns?

 Assessee Due date 1. Where the assessee is a company, who is required to get his accounts audited under IT Act 30th September 2. Where the assessee is a person, other than a company, who is required to get his accounts audited 30th September 3. In another case other than 1 & 2 31st July

Question 3.
Write note on filling e-return.
The return is not uploaded with DSC, the ITR-V Form should be printed, signed and submitted to CPC within 120 days from the date of e-Filing. The return will be processed only upon receipt of signed ITR-V. Please check your emails/SMS for reminders on non-receipt of ITR-V.

Upload Income Tax Return process is complete now.
Prepare and Submit ITR Online
Go to e-File and click on “Prepare and Submit ITR Online”.
Only ITRs 1 and 4s can be filled online
Select the Income Tax Return Form ITR 1/ITR 4S and the Assessment Year.
Fill in the details and click the “Submit” button.
Upload Digital Signature Certificate (DSC), if applicable.
Please ensure the DSC is registered with e-Filing.
Click on “Submit” button.
On successful submission, ITR-V would be displayed (if DSC is not used). Click on the link and download the ITR-V. ITR-V will also be sent to the registered email. If ITR is uploaded with DSC, the Return Filing process is complete.

Question 4.
Explain the general uses of PAN.
a) Since PAN Card contains information such as Name, Age and photograph, it can be used throughout the country as a valid identity proof.

b) PAN is the best possible way to keep track of your tax payment. Otherwise, you might be required to pay it multiples times since your tax payment cannot be verified.

c) Since PAN is unique for every entity, its misuse is almost impossible for purposes of tax evasion or other devious meAnswer:

d) PAN Card can be used to avail utility connections such as electricity, telephone, LPG, and internet.

Question 5.
Explain the different types of digital signature.
There are two types of Digital Signature Certificate.
1. PFX File
PFX file is a Digital Signature Certificate that is in a file format (pfx format). This type of signature can be easily circulated through e-mail, which makes it easier for usage. However there is a risk of misuse, if not handled properly.

2. USB Token
Digital Signature certificate in a USB Token, looks similar to a pen drive, which is … attached to the PC for using digital signature. The main advantage of it is that it safeguards DSC from misuse, which is more likely in pfx file.

Question 6.
Write note on due date and rate of advance tax payment.
A The advance tax is to be paid in the following installments on the following dates:
For Non-Corporate Assessee
On or before 15 September – not less than 30% of tax payable for the year
On or before 15. December – not less than 60% of tax payable for the year.
On or before 15 March – not less than 100% of tax payable for the year

For Corporate Assessee
On or before 15 June – not less than 15% of tax payable for the year
On or before 15 September – not less than 45% of tax payable for the year
On or before 15 December : – not less than 75% of tax payable for the year
On or before 15 March – not less than 100% of tax payable for the year

Practical Problems

Question 1.
Compute the amount of TDS on Salary to be deducted of Mr. Anad whose Total taxable income from Salary after deductions u/s 80 is ₹ 10,00,000.
TDS = Average rates i.e. total income/12
TDS = 10,00,000/12
= ₹ 83,333 + Cess 4%
= ₹ 86,666

Question 2.
From the following details of income compute TDS amount for each transaction:
a) Winning from lottery ₹ 2,00,000
b) Dividend from listed company ₹ 40,000
c) Mr. Raju agent of LIC earned a commission of ₹ 30,000
d) Rent paid on Building 25,000 per month
e) LIC amount paid to the policy holder by company on maturity ₹ 3,00,000
f) Interest on bank deposits ₹ 40,000
g) Winning from Horse race₹ 5,000

Question 3.
From the following details of income compute TDS amount for each transaction:
a) Winning from lottery ₹2,00,000
b) Dividend from listed company ₹ 70,000
c) Mr. Sanju agent of LIC earned a commission of ₹ 40,000
d) Rent paid on Building ₹ 38,000 per month
e) LIC amount paid to the policy holder by company on maturity ₹ 5,00,000
f) Interest on bank deposits ₹ 10,000
g) Withdraw of premature employee provident fund ₹ 90,000 without furnishing PAN
h) Winning from Horse race ₹ 10,000
i) Compensation for acquisition of Land ₹ 3,40,000

Question 4.
From the following details of income compute TDS amount for each transaction:
a) Winning from puzzle ₹ 16,000
b) Lump sum Payment to a contractor X Ltd., ₹ 50,000
c) Dividend from a company other hand listed company ₹ 90,000
d) Interest on securities ₹ 25,000
e) Commission earned by an insurance agent ₹ 76,000
f) Sale of Building ₹ 65,00,000
g) Withdraw from National Savings Scheme ₹ 7,000
h) Rent paid on Building ₹ 97,000 per month
i) LIC amount paid to the policy holder by company on maturity ₹ 3,00,000
j) withdraw of premature employee provident fund ₹ 65,000

Question 5.
From the following details of income compute TDS amount for each transaction:
a) Sale of land to a resident ₹ 77,00,000 without furnishing PAN
b) Compensation for acquisition of building ₹ 3,65,000.
c) Commission earned on sale of lottery tickets ₹ 65,000
d) Technical fees collected ₹ 45,000
e) Annual Salary ₹ 3,50,000
f) Winning from Lottery ₹ 75,000
g) LIC payment to policy holder ₹ 8,00,000
h) Payment made to a contractor Mr. B. is ₹ 20,000 however the total payment in FY ₹ 2,20,000

Question 6.
From the following details of income compute TDS amount for each transaction:
a) Withdraw from EPF by an employee who has worked for 3 years ₹ 60,000 furnishing PAN
b) Dividend from unlisted company ₹ 7,000
c) Winning from horse race ₹ 18,000
d) Commission on insurance earned by agent ₹ 36,000
e) Withdraw from National Saving Scheme ₹ 5,000
f) Rent paid to building ₹ 3,40,000 p.a.
g) Rent paid to land lord ₹ 45,000 per month
h) Dividend from Indian company listed in BSE ₹ 4,000
i) Winning from lottery ₹ 2,00,000

Question 7.
Calculate the TDS to be made in respect o the following transactions for F. Y. 2018-19 (A. Y. 2019-20)
a) Salary estimated for the year ₹ 4,20,000 and income from other sources ₹ 1,20,000 (both taxable)
b) Gross winnings from lottery ₹ 45,000
c) Gross amount from Horse race ₹ 4,000
d) Insurance commission ₹ 25,000
e) Commission on sale of lottery tickets ₹ 7,000
f) Interest on securities ₹ 12,000
a) Taxable salary estimated – ₹ 4,20,000
Taxable income from other sources – ₹ 1,20,000
GTI/NTI – ₹ 5,40,000
Income Tax:
Upto 2,50,000 – NIL
Next 2,50,000 @ 10% – 25,000
Balance 40,000 @ 20%- 8,000 33,000
Add: Health & Education Cess @ 4% 1,320
Total 34,320
Per month TDS = 34,320/12 = ₹ 2,860
b) Gross winnings from lottery = 45,000, TDS @ 30% × 45000 = 13,500
c) Gross winnings from Horse Race 4,000, No TDS as its below ₹ 10,000
d) Insurance commission ₹ 25,000, TDS 25,000 × 5% = ₹ 1,250
e) Commission on sale of lottery = ₹7,000, NO TDS as its below ₹ 15,000
f) Interest on securities ₹ 12,000, TDS = 12,000 × 10% = ₹ 1,200

Question 8.
Calculate TDS in the following cases:
a) Compensation for the acquisition of land ₹ 5,00,000
b) Rent received ₹ 60,000 per month on building
c) Amount from RPF on premature settlement ₹ 70,000
d) Interest on deposits with a firm ₹ 28,000.
e) Amount paid to civil contractor ₹ 20,000 but the aggregate amount during the year exceeds one lakh rupees and contractor is PQR Ltd.
f) Commission on sale of house ₹ 80,000
g) Interest on securities Gross ₹ 22,000
a) Compensation for land acquisition ₹ 5,00,000, TDS = 5,00,000 × 10% = 50,000
b) Rent received ₹ 60,000 per month, TDS = 60,000 × 5% = 3,000 per month
c) RPF amount on premature settlement ₹ 70,000, TDS = 70,000 × 10% = 7,000
d) Interest on deposit with firm ₹ 28,000, TDS = 28,000 × 10% = 2,800
e) Payment to PQR Ltd., contractor exceeding ₹ 1,00,000 per annum ₹ 20,000 TDS 20,000 × 2% = 400
f) Commission on sale of house = ₹ 80,000, TDS 80,000 × 5% = 4,000.
g) Interest on securities = 22,000, TDS = 22,000 × 10% = 2,200

Question 9.
Calculate TDS in the following cases:
a) Amount of gross income from house race ₹ 1,50,000
b) Interest on securities ₹ 28,000
c) Amount from premature withdrawal of provident fund ₹ 85,000
d) Insurance commission ₹ 24,000
e) Paid to sanitary contractor Mr. Ramakonnta Reddy, Gross ₹ 39,000
f) Amount from sale of immovable property ₹ 30,00,000
g) Amount from life insurance policy ₹ 90,000
h) Amount paid to lawyer 80,000
a) Race amount ₹ 1,50,000, TDS 1,50,000 × 30% = 45,000
b) Interest on securities 28,000, TDS 28,000 × 10% = 2,800
c) Amount from premature withdrawal ₹ 85,000, TDS 85,000 × 10% = 85,00
d) Insurance commission 24,000, TDS = 24,000 × 5% = 1,200
e) Payment contractor ₹ 29,000, TDS = 29,000 × 1% = 2,900
f) Amount from sale of immovable property ₹ 2,00,000, NO TDS as its below 5,00,000
g) Amount from LIC policy ₹ 70,000,
NO TDS as its below ₹ 1,00,000
h) Amount paid ₹ 80,000 to lawyer, TDS = 80,000 × 10% = 8,000

Question 10.
XYZ Co. Ltd. has an estimated total tax liability of 1,50,000 for the P.Y. 2018-19.
(i) What are the due dates for the payment of advance tax?
(ii) What is the amount of advance tax to be paid on each due date?
Due dates for the payment of advance tax
On or Before 15th June
On or Before 15th September
On or Before 15th December
On or Before 15th March
Amount of advance fax to be paid on each due date
Upto 15-06-2018 = 15% × 1,50,000 = 22,500
Upto 15-09-2018 = 30% × 1,50,000 = 45,000
Upto 15-12-2018 = 30% × 1,50,000 = 45,000
Upto 15-03-2019 = 25% × 1,50,000 = 37,500
Total = 1,50,000

Question 11.
Mr. Amar Gupta has the following estimated incomes for FY 2018-19.
Salaries (Taxable) = 9,00,000
Income from HP (Taxable) = 4,00,000
Income from other sources – Interest on securities (Taxable) = 1,00,000

Question 12.
Arnav & Sons a firm, has an estimated taxable business income of ₹ 4,80,000 and taxable STCG of ₹ 1,20,000 on 03-06-2018. Calculate advance tax in statements if the TDS is estimated to be ₹ 18,480 for the financial year 2018 – 19.

Question 13.
Find out the amount of advance tax payable by Ananya on specified dates for the F.Y, 2018-19;
Business Income (Tax of ₹ 544 is deducted at source) ₹ 4,91,000
Agricultural income ₹ 86,000

Question 1.
Define Custom Act 1962.
This duty is the main act which provide for levying and collection of duty, import or export, procedure, prohibition on importation and exportation of goods, penalties, offences etc.

Question 2.
State any two objectives of Customs Act, 1962.
The two objectives of Customs Act, 1962 are:

1. To regulate imports and exports
2. To protect Indian industry from dumping
3. To collect revenue from Custom Duty
4. To prevent illegal imports and export of goods (smuggling).

Question 3.
Define Custom Tariff Act 1972.
This act contains two schedules. Schedules are as follows:
Schedule 1:
Gives classification and grades of duty for imports.
Schedule 2:
This classification and trades of duty of exports.

In addition this act gives provisions for levying duty like additional duty, anti-dumping duty, prefential duty, protective duty.

Question 4.
Give the meaning of custom duty?
Custom duty refers to the duty levied on import of goods and export of goods.

Question 5.
List out objectives of custom duty.
i) Raising revenue for Central Government
ii) Regulate imports and exports
iii) Protect Indian industries from dumping
iv) Prevention of Smuggling.
v) International passenger processing.

Question 6.
State different types of custom duty.
The different types of custom duty are:

1. Basic Customs Duty
3. Education Cess on Customs duty
4. Protective duties
5. Countervailing duty on subsidised goods

Question 7.
CBEC – Central Board of Excise & Customs BCD – Basic Customs Duty

Question 8.
What are Dutiable goods under Customs Act-1962.
According to Section 2 (14) of the Customs Act, dutiable goods’ are those goods which are chargeable to duty and on which duty has not been paid. Thus, goods remain ‘dutiable’ till they are not cleared from the port.

Question 9.
What is ‘tariff value’ under Customs Act?
Tariff value can be fixed by CBE&C (board) for any class if import goods or export goods. Govt. should consider trend of value of such or like goods which fixing tariff value.

Question 10.
What is assurable value in customs?
Assessable value is the total of CIF (Cost, Insurance and Freight) value of item in local currency. This is the sum of total FOB (Free On Board) item value, freight, insurance, and other charges.

Question 11.
What is value for the purpose of levy of customs duty?
Customs duty is payable as a percentage of ‘Value’ often called ‘Assessable Value’ or ‘Customs Value’. The Value may be either (a) ‘Value’ as defined in section 14(1) of Customs Act or (b) Tariff value prescribed under section 14(2) of Customs Act (section amended w.e.f.1010-2007).

Question 12.
What is transaction value?
Transaction value of imported goods shall be the price actually paid or payable for goods when sold for exports to India, adjusted in accordance with provisions of rule 9.

Question 13.
What is anti-dumping duty?
Anti dumping duty is a kind of imposed duty which is charged on any article of import to India at less than its normal value not exceeding the margin of dumping in relation to such article.

Question 14.
What Is remission of duty?
Remission means waiver or cancellation of excise duty legally payable. Section 5 of the Act provides that Central Government can provide for remission of duty of excise payable on excisable goods, which due to any natural clause, are found to be deficient in quantity, by making rules in that behalf.

Question 15.
Define Entry.
In relation to goods means an entry made in a bill of entry, shipping bill of export and includes in the case of goods imported or to be exported by port the entry referred to in sec 82 or the entry made under the regulations made under sec 84.

Question 16.
What is Custom Station?
Custom Station is a part of Customs area which includes any area where imported goods or export goods are ordinarily kept pending for clearance by Customs authorities. Custom station means:

1. Customs port
2. Inland container depot
3. Customs airport
4. Land customs station

Question 17.
Give the meaning of customs area.
Means the area of a custom station and includes any area in which imported goods or export goods are ordinarily kept before clearance oy customs authorities.

Question 18.
Who is an exporter?
In relation to any goods, at any time between their entry for export and the time when they are exporter, includes any owner or any person holding himself out to be the exporter.

Question 19.
Who is an importer?
In relation to any goods at any time between their importation and the time when they are cleared for home consumption, includes any owner or any person holding himself out to be the importer.

Question 20.
What is dutiable goods?
As any goods which are chargeable to duty and on which duty and on which duty has not been paid thus, goods continue to be dutiable till they are not cleared from the customs port however, once goods are assessed at nil rate of duty, they no longer remain dutiable goods.

Question 21.
Give the meaning of exported goods.
Export goods means any goods which are to be taken out of India goods brought near customs area for export purpose will be export goods.

Question 22.
Give the meaning of imported goods.
Imported goods as goods brought in India from a place outside India, but do not include goods which have been cleared for home consumption. Thus, once goods are cleared for home consumption by customs authorities from custom area, they are no longer imported goods.

Question 23.
Give the meaning of Transit goods.
Sec.53 Provide that any good, imported in any conveyance will be allowed to remain con conveyance without payment of custom duty, to any place out of India or custom duty, to any place out India or custom station.
However, all these goods must be mentioned in import manifest submitted by person incharge of the conveyance.

Question 24.
Give the meaning of entry inward.
After delivery of import manifest or if custom officer is satisfied that there are sufficient reasons for not delivering the import manifest, custom officer shall grant entry inward U/S 31

Question 25.
What do you mean by entry outward?
The vessel intending to start loading of export goods; for outward movement should be granted entry outward by custom officer U/S 32

Question 26.
What is duty drawback?
Duty drawback is a kind of duty which is given back to the exporter of finished products if they are not able to avail any kind of refund of duty paid on inputs.

Question 27.
What do you mean by green channel?
Green Channel is the procedure for clearance of goods under this facility is following

1. Importer has to make a declaration in the declaration form at the time of filing of bill of entry.
2. The appraisement is done as per normal procedure except that there would be no physical examination of the goods only mark and number are to be checked.

Question 28.
State various types of Customs Duty.
The various types of Customs Duty are:
BCD, CVD, Special CVD, NCCD, Anti-Dumping Duty, Safeguard Duty, Protective Dugy.

Question 29.
Expand BED and BCD.
BED – Basic Excise Duty
BCD – Basic Customs Duty

Question 30.
Expand NCCD and SAHEC.
NCCD – National Calamity Contingent Duty
SAHEC – Secondary and Higher Education Cess

Question 1.
List the objectives of levying custom duty.
Following are the objectives of custom duty:

1. Raising revenue for Central Government
2. Regulate imports and exports
3. Protect Indian industries from dumping
4. Prevention of Smuggling.
5. International passenger processing.

Question 2.
Write short not eon BCD.
Basic Customs Duty: This is the duty levied under Section 12 of Customs Act Normally it is levied as a percentage of Value as determined under Section 14(1). The rates vary for different items, but general rate on non-agricultural goods at present is 15%. w.e.f. 01.03.2005. (It was 20% w.e.f. 9.10.2004)

To protect Indian agricultural and Indian automobile sector, duties on some articles is higher. Duty on liquor is also high.

Question 3.
Write a short note on the levy of custom duty.
Entry 83 to List I – (Union List) of Seventh Schedule to Constitution reads ‘Duties of customs including export duties’. Thus, import and export duty is a Union subject and power to levy is derived from Constitution. Section 12 of Customs Act, often called charging section, provides that duties of customs shall be levied at such rates as may be specified under ‘The Customs Tariff Act, 1975′, or any other law for the time being in force, on goods imported into, or exported from India. Thus, Goods become liable to import duty or export duty when there is import into, or export from India’.

As per section 2(28), ‘export’ with its grammatical variations and cognate expressions, means taking out of India to a place outside India.
As per section 2(23), ‘import’ with its grammatical variations and cognate expressions, means bringing into India from a place outside India

Section 2(27) of Customs Act defines ‘India’ as inclusive of territorial waters. Hence, it was thought that ‘import’ is complete as soon as goods enter territorial water. Similarly, : export is complete only when goods cross territorial waters.

In Garden Silk Mills Ltd. v. VOI 1999(b) SCALE 285 = 1999 AIR SCW 4150 = 1999(113) ELT 358 = ZT 1999(7) SC 522′ = AIR 2000 SC 33 [SC. 3 member bench] – it was held hat import of goods in India commences when they enter into territorial waters but continues and is completed when the goods become part of the mass of goods within the country. The taxable event is reached at the time when the goods reach customs barrier and bill of entry for home consumption is filed.

Taxable Event
According to charging section, makes it clear that importation or exportation of goods into or out of India is taxable event for payment of duty of customs. Thus charge of duty is on importation or exportation of goods not on person importing or exporting.

Question 4.
What are the exemptions of duty under Customs Act?
The exemptions are as follows
(i) Exemptions by Notification (Sec 25(1)): Section 25 (1) of Customs Act, 1962 authorises Central Government to issue notifications granting exemptions from duty. Such exemptions may be unconditional or subject to certain conditions. Such conditions may be required to be fulfilled before or after clearance. Government can also grant exemption by a special order in exceptional circumstances. The exemption notification should be published in gazette and should be issued only in ‘public interest’.

(ii) Exemption by special order (Adhoc exemption) (Sec 25(2)): Sections 25(2) of Customs Act permit Government to issue ad-hoc exemption from customs duty by issue of a special order in exceptional circumstances for granting ad hoc exemption. It has been clarified that such exemption can be granted even after duty is paid. In such case, duty has to be refunded.

(iii) Exemption for past general practice (Sec 28A): If there was past general practice of exempting certain goods from customs duty, but later it is discovered that, in fact, customs duty was payable Government can grant exemption with retrospective effect

(iv) Exemption to minor amounts of customs duty (Sec 25(6)): Customs duty. is not payable if amount of duty is Equal to or less than 100

Question 5.
What are the dutiable goods under Customs Act -1962?
Customs duty is on ‘goods’ as per Section 12 of Custom Act. The duty is payable on goods belonging to Government as well as goods not belonging to Government.
Section 2(22) gives inclusive definition of ‘goods’ as follows:

1. Vessels, air crafts and vehicles
2. Stores
3. Baggagteo 190.000
4. Currency and negotiable instruments
5. Any other kind of movable property

All goods mentioned above on which Customs duty can be levied are called as dutiable goods.
Section 2(14) defines dutiable goods’ as any goods which are chargeable to duty and on which duty has not been paid. Thus, goods continue to be ‘dutiable ‘ till they are not cleared from the port. However, once goods are assessed as ‘Nil’ rate of duty. They no more remain dutiable goods.

Question 6.
What are the basis of different methods of valuation for customs?
The Valuation Rules, 1988 based on WTO Valuation Agreement, consists of rules providing six methods of valuation.
These methods are to be applied in sequential order i.e. if method

1. Cannot be applied, then method.
2. Comes into force and when method.
3. Cannot be applied, then method.
4. Should be adopted. The only exception is that the ‘computed value’ method may be adopted/used before ‘deductive method’, if the importer requests and Assessing Officer permits.

These methods are explained as follows:
1) Transaction value of imported goods: Transaction value of imported goods shall be the price actually paid or payable for the goods when sold for export to India, adjusted in accordance with provision of rule 9. As per rule 9, various additions like cost of containers, cost of packing, cost of materials, components etc. or services supplied by buyer; royalties payable etc. are includible, if these do not already form part of transaction value.

2) Transaction value of identical goods: ‘Identical goods’ are defined under rule 2(1)(C) as those goods which fulfill all the following conditions:

1. Goods should be same in all aspects.
2. Goods should have been produced in the same country.
3. They should be produced by same manufacturer.

Rule 5 of Customs valuation Rules provide that if valuation on the basis of ‘transaction value’ is not possible, the ‘Assessable Value’ will be decided on basis of transaction value of identical goods sold for export to India and imported at or about the same time, subjected to necessary adjustment.

3) Transaction of similar goods: If first and second method of transaction value of goods and identical goods respectively cannot be used, rule 6 provide for valuation on the basis of ‘Transaction value of similar goods improved at or about the same time.
Similar goods are those which are: alike in all respects, produced in the same country by the same manufacturer.

4) Deductive Value: Rule 7 of Customs Valuation Rules provide for the next i.e. fourth alternative method i.e. ‘deductive method’. This method should be applied if transaction value of identical goods or similar goods is not available; but these products are sold in India. The sale should be in the same condition as they are imported. Assessable value is calculated by reducing post importation costs and expenses, from this selling price. This is called deductive value because assessable value has to be arrived at by method of deduction (deduction means arrive at by inference by making suitable additions, subtractions from a known price to arrive at required Customs Value’

5) Computed Value for Customs: If valuation is not possible by deductive method, the same can be done by computing the value under rule 7A, which is the fifth method. If the importer requests and the customs officer approves, this method can be used before the method of ‘deductive value’. In this method, value is the sum of
a) cost of value of materials and fabrication or other processing employed in producing the imported goods,

b) an amount for profit and general expenses equal to that usually reflected in sales of goods of the same class or kind, which are made in the country of exportation for export to India.

6) Residual method: The sixth and the last method is called ‘residual method’. It is also often termed as fall back method. This method is used in case where ‘ Assessable value’ cannot be determined by any of the preceeding methods. While deciding assessable value under this method, reasonable means consistent with general provisions of these rules should be the basis and valuation should be on the basis of data available in India.

Question 7.
What are the various types of customs duty?
Types of Custom Duty
1. Basic Customs Duty: This duty is imposed on the value of goods at a specified rate as it is fixed on an ad-valorem basis. After being amended time and again, it is currently regulated by the Customs Tariff Act, 1975. The Central Government, however, holds the rights to exempt specific goods from this tax.

2. Countervailing Duty: CVD or Additional Customs Duty is levied on imported goods that fall under Section 3 of the Customs Tariff Act of 1975. It is the same as the Central Excise Duty which is levied on similar goods that are produced in India.

3. Protective Duty: This duty is imposed in order to shield the domestic industry against the imports, at rates that are recommended by the Tariff Commissioner,

4. Safeguard Duty: As the name suggests, this duty serves as a means of safeguarding the rise in exports. Sometimes, if the government feels that a rise in exports can damage the existing domestic industry, it may levy this duty.

5. Anti-Dumping Duty: This duty is based on the dumping margin, i.e. the difference between the export price and the normal price. It is only imposed when the goods that are imported are below the fair market price.

Section-B & C (Practical Problems)

Question 1.
From the following information calculate assessable value
FOB = 8000 UK pounds
BCD = 10%
Exchange rate notified by CBE and ₹ 56 = 1 pound
Exchange rate announced by RBI ₹ 55 = 1 pound

Question 2.
From the following particular determine the assessable value of the imported equipment giving explanation for each item
a. FOB cost of equipment (Japanese Yen) 1,00,000 Yen
b. Freight charges in Japanese Yen 10,000 Yen
c. Charges for development connected to equipment paid in India 30,000
d. Insurance charges paid in India for transportation from Japan 10,000
e. Commission payable to agent in India 12,000.
f. Exchange rate as per RBI is 1 Yen = ₹ 0.58 Exchange rate as per CBE & C 1 Yen = 0.60. Landing charges 1 % of CIF cost.

Question 3..
From the following information, compute the assessable value:
(i) Value of Machine in UK pounds 32,000. FOB
(ii) Engineering and design charges paid – UK pounds 12,000
(iii) Freight paid (Air) – UK pounds 6000
(iv) Insurance – Not Known
(vi) The exchange rate announced by the Central Government is ₹ 68 per UK pound.

Question 4.
Vedant Ltd., an actual user imports certain goods from California at Chennai port, at cost of $1,00,000 FOB. The other details are as follows: i) Packing charges:$ 22,000.
ii) Sea freight to Indian port: $28,000. iii) Transit insurance:$ 10,000.
iv) Design and development charges paid to a consultant in USA by importer: $9,000. v) Selling commission to be paid by the Indian importer: ₹ 5,000. vi) Rate of exchange announced by RBI: ₹ 59.5 per$.
vii) Rate of exchange notified by the Central Board of Excise and Customs: 60 per $. Rate of basic custom duty: 15%. Compute the assessable value of the imported goods and the basic customs duty payable. Question 5. ABC Ltd. imported goods from USA at a cost of US Dollars 19,000 FOB. The I other details are as follows: a) Transit insurance — 1,900 dollor b) Commission to local agent — 5,800 c) Sea freight charges — 5,500 dollor d) Packing charges — 4,300 dollor e) Design and development charges of 5,000 dolloars were paid to consultancy firm in USA. f) Rate of exchange notified by CBE and C ₹ 58 = 1 dollar g) Rate of exchange announced by importer bank ₹ 59 = 1 dollor Compute assessable value of the imported goods. Question 6. An importer has imported a machine from japan at FOB cost of 13,00,000 Yens. Other details are as follows: a) Freight from Japan to Indian port was 18,000 Yens. b) Transit insurance charges were 1% of FOB value. c) Design and development charges of 95,000 Yens were paid to a consultancy firm in Japan for design of machinery. d) Packing charges of 25,000 Yens were charged extra e) ₹ 24,000 was spent in design cost on machine in India. f) An amount of 95,500 Yens was payable to Japanese manufacturer towards charges for installation and commissioning the machine in India. g) Rate of exchange as announced by RBI was: 1 yen = ₹ 0.405. h) Rate of exchange as announced by Central Government by notification under Section 14(3)(a)(i): 1 Yen = 0.401 ₹ i) Customs duty was 20%. Find the customs duty payable. Question 7. Mr Bharath imports by air from USA a machine along with relevant accessories e and spares for the value US$ 1,20,000 FOB. The others details are as follows:
(a) Commission to local agent in India ₹ 27,000
(b) Freight and Insurance from airport to factory go down ₹ 30,000
(c) Freight – US $36,000 (US to India) (d) Goods are insured, premium amount is not shown in invoice and not available (e) At the request of Mr. Bharath, US$ 6000 has been incurred as expenses for improving the design of the machine, but the same is not reflected in the invoice.
(f) Basic custom duty is 15%, Social Welfare Surcharge 10% and IGST – 18%
(g) Exchange rate to be considered US $1 = ₹72 Question 8. Compute the Customs duty from the following data (i) Machinery imported from USA by Air (FOB) 4,000 US$,
(ii) Accessories were compulsorily supplied with Machine (Electric Motor & others) (FOB) 1,000 US $, (iii) Air freight 1,500 US$
(iv) Insurance 50 US $, (v) Local agents commission to be paid in Indian Rupees is 36,000 (say equivalent to US$ Dollars 100),
(vi) The exchange rate is 1 US Dollars = Indian Rupees is 60
(vii) Customs duty on Machinery -10% ad valorem.

Question 9.
A person makes an unauthorised import of 1000 pieces of ophthalmic rough blanks CIF priced at $1 per piece by air from USA (Tariff heading 70.1510). The consignment is liable to be confiscated. Import is adjudicated. AC gives to the party an opinion to pay fine in lieu of confiscation. It is proposed to impose fine equal to 50% of margin of profit. The market price is * 100 per piece of ophthalmic rough blank. The rates of duty are – Basic customs – 10% Health and Education cess – as applicable, Exchange rate is –$ 1 = ₹ 45. Compute
i) Amount of fine.
ii) Total payment to be made by party to clear the consignment. What is the maximum amount of fine that can be imposed in this case? Quote section.
iii) What are the duty refunds/benefits available if the importer is
(a) Manufacturer
(b) Service provider

Question 10.
A consignment is imported by Air, CIF price is 2500 US dollars. Air freight is 600 US dollars and insurance cost is 75 US dollars. Exchange rate announced by CBE & C as per customs notification is 1 US dollar = ₹65. Basic custom duty payable is 10%. Social Welfare Surcharge is applicable. IGST at the rate of 18%. Find the value for customs purpose and total customs duty payable.

Question 11.
A company imported a machine from. USA of CIF. price is 3,300 dollors.
From the following information determine the assessable value and customs duty payable.
i) Freight from America to Indian airport 330$ii) Insurance 75$
iii) Design and development charges paid to consultancy firm in USA 1000$iv) The company also spent an amount of ₹ 6,600 in India for installation of machine. v) Exchange rate as notified by CBE and C is 65.50 = 1$ .
vi) BCD payable is 13%
vii) Social Welfare Surcharge at 10%

Question 12.
Determine the total customs duty payable from the following data: quantity imported: 100MTS, FOB value; Swiss Franc: 10,000, Air Freight: swiss franc: 2,500 Insurance: Data not available, exchange rate: 1 swiss Franc = ₹ 34, rate of BCD 15%, Social Welfare Surcharge applicable.

Question 13.
Determine the assessable value and payable custom duty for the purpose of customs act 1962 from the following Information in respect of import of a machine form UK:
i. FOB value UK Pound 6,000
ii. Air Freight UK Pound 1,500
iii. Design and Development charges paid in UK Pound 500
iv. Design and Development charges paid in India ₹ 10,000
v. Commission paid to local agents 1 % of FOB value
vi. Date of Bill of entry 10-04-2018 (exchange rate notified by CBEC UK Pound 1 = ₹ 70)
vii. Date of entry Inward 20-04-2018 (exchange rate notified by CBEC UK pound 1 = ₹ 65).
viii. BCD at 20% and basic customs IGST at 18%.

Question 1.
What is progression?
A sequence that consists of a set of numbers arranged using some precise rule is called progression. It is also arranged in a sequence, which can be determined on the type it is being arranged.

Question 2.
Define arithmetic progression.
A sequence of numbers in which the first term is a constant and after the first term, each term is obtained by adding a constant number to the preceding term is always the same.
E.g.: 2, 4, 6, 8 …. is an A.P. where the first term is 2 and the common difference is 2.

Question 3.
What is a finite series?
If the number of terms in a sequence is limited then it is said to be as a finite series.
E.g.: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
The number of terms in the above series is 8, so it is a finite series.

Question 4.
What is an infinite series?
If the number of terms in a sequence is unlimited and they are connected by any sign ‘+’ or ‘n’ then the series of terms is called the infinite series.

Question 5.
What is common difference?
The difference between any two numbers in a series of A.P is called common difference. In other words, common difference in any term minus preceding term.

Question 6.
What is a GP? Give an example.
Geometric Progression (GP) is a sequence whose terms increase or decrease by a common constant ratio called the C.R. E.g.: 2, 4, 8……

Question 7.
What is common ratio in geometric progression?
The fixed constant of ratio of each term of a geometric progression to the term preceeding is called common ratio.

Question 8.
Distinguish between an arithmetic progression and geometric progression.
Arithmetic progression is a sequence of numbers in which the difference of any term and its proceedings is constant. The constant difference is known as common difference whereas geometric progression is a sequence of numbers in which the ratio of any two consecutive number is constant. The constant ratio is called common ratio.

Problems for 2 Marks

Question 1.
Find the 8th term of the sequence 2, 4, 6, …..
The given sequence is an A.P.
The common difference, d = 4 – 2 = 6 – 4 = 2
∴ the nth term = a + (n – 1)d
i.e., tn = a + (n – 1)d
a = 2 d = 2 n = 8
Here 8th term = t8 = 2 + (8 – 1) 2
= 2 + 7 × 2
= 16
∴ 8th term of the given A.P. is 16.

Question 2.
Find the 15th term of an A.P. 1, 3, 5……
The common difference, d = 3 – 1 = 2; 5 – 3 = 2
∴ The nth term
tn = a + (n – 1)d
∴ 15th term = t15 = 1 + (15 – 1) 2 = 1 + 14 × 2 = 29

Question 3.
Find the 10th term of a sequence 10, 12, 14……
10th term of a sequence 10,12,14…….
Given sequence is an A.P.
Common difference,
d = 12 – 10 = 14 – 12 = 2
The nth term = 1 + (n – 1)d
i.e, tn = a + (n – 1)d
Here, 10th term = tn = 10 + (10 – 1)2 = 10 + 18 = 28
∴ 10th term of the given A.P. is 28

Question 4.
Which term of the series 7, 10, 13……..is 151 ?
Tn = a + (n – 1)d
⇒ 151 = 7 + (n – 1)3 ⇒ 151 = 7 + 3n – 3
⇒ 151 = 4 + 3n = 3n = 147
⇒ n = 49
∴ 49th term is 151

Question 5.
Find the 12th term of the series 30 + 35 + 40 + 45 + …..
The given series is an A.P.
Here, first term, a = 30 and common difference, d = 35 – 30 = 40 – 35 = 5
∴ Then nth term, tn = a + (n – 1)d
Putting n = 12, a = 30 + (12 – 1)5
12th term, t12 = 30 + (12 – 1)5 = 30 + 11 × 5
= 30 + 55 = 85

Question 6.
Find the 45th term of the series 3, 6, 9, …..
The given series is an A.P.
Here, first term, a = 3 and common difference d = 6 – 3 = 3
∴ Then nth term, tn = a + (n – 1)d
Putting n = 45, a = 3 and d = 3, we get
45th term, t45 = 3 + (45 – 1)3 = 3 + 44 × 3 = 3 + 132 = 135

Question 7.
Find the 10th term of the A.P. 3, 6, 9, ….
The given series is an A.P.
Here, First term a = 3 and the common difference d = (6 – 3) or (9 – 6) = 3
∴ The nth term Tn = a + (n – 1)d
Putting n = 10, a = 3, d = 3 we get
10th term = 3 + (10 – 1)3
= 3 + 9 × 3 = 3 + 27 = 30
∴ 10th term of the A.P. is = 30

Question 8.
Find the 10th term of the series 1.2 + 1.7 + 2.2 + ………….
The given series is an A.P. First term, a = 1.2
Common difference, d = 1.7 – 1.2 = 0.5
The nth term, t = a + (n – 1)d
Putting n = 10, a = 1.2, d = 0.5 we get
t10 = 1.2 + (10 – 1) (0.5)
= 1.2 + 9 × 0.5 = 1.2 + 4.5 = 5.7

Question 9.
What term of the following A.P. is 90. 3 + 6 + 9 + 12 + …………….
The given series is an A.P. where,
First term a = 3
Common difference, d = 6 – 3 = 3
∴ The nth the term, tn = a + (n – 1)d
= 3 + (n – 1)3 = 3 + 3n – 3 = 3n
Suppose the nth term is 90
Then 90 = 3n ⇒ n = $$\frac{90}{3}$$ ∴ 90 is 30th term.

Question 10.
Which term of the series 15 + 12 + 9 + 6 + … is equal to -90?
The given series is an A.P. where a = 15, d = 12 – 15 = -3
tn = a + (n – 1)d
⇒ -90 = 15 + (n – 1)(-3) = 15 – 3n + 3 = -90
⇒ -3n = -90 – 18 = -3n = – 108
⇒ n = $$\frac{-108}{-3}$$
∴ n = 36

Question 11.
Find the 17th term of the series 3, 6, 9, 12,…
Here, a = 3, d = 6 – 3 = 3, n = 17
tn = a + (n – 1)d
t17 = 3 + (17 – 1) × 3 = 3 + 48 = 51
17th term of the series = 51

Question 12.
Is 63 a term of the series 5 + 10 + 15 + 20….
Let the nth term is 63
Here, a = 5, d = 10 – 5 = 5
We know, tn = a + (n – 1)d
⇒ 63 = 5 + (n – 1)5 ⇒ 63 = 5 + 5n – 5
⇒ 63 = 5n ⇒ n = 12.6
This is not possible, because n must be a whole number.
So, there is no term equal to 63.

Question 13.
Find the 6th term of G.P. 2, 6, 18…….
a = 2, r =3, n = 6
tn = arn-1
t1 = 2
t2 = 6 = 2r = 6/2 = r = 3 = r
t6 = ar5 = 2 × (3)5 = 2 × 243
t6 = 486
The 6th term of G.P. 486

Question 14.
Find the 6th term of GP 5, 15, 45, …
a = 5, r = 3, n = 6
tn = arn-1 = 5(3)5 = 1215

Question 15.
Find the common ratio of the G.P 5, $$\frac{5}{2}, \frac{5}{4}$$…
Common ratio = $$\frac{\text { Any term }}{\text { Previous term }}$$ =$$\frac{\frac{5}{2}}{5}$$ = $$\frac{1}{2}$$

Question 16.
Find the 7th term of the sequence 2, 4, 8, …..
Any term The given sequence is the G.P. Common ratio = $$\frac{\text { Any term }}{\text { Previous term }}$$ = $$\frac{8}{4}$$ = 4
We know, nth term, Tn = arn-1
where, a is the first term and r is the common ratio
∴ t7 = 2 x (2)7-1 = 2 × 26 = 2 × 64 = 128

Question 17.
Find the 8th term of the G.P. 5, 15, 45, …
tn = arn-1 ⇒ 5(3)8-1 ⇒ 5(3)7 ⇒ 5 × 2187 ⇒ t8 = 10935

Problems on Arithmetic Progression

Question 1.
Find the 12th term of the sequence, 1.5, 3, 4.5, 6, …
The given sequence is in A.P.
Given the first terim, a = 1.5
Common difference, d = 3 – 1.5 = 1.5
∴ The nth term tn = a + (n – 1)d
Substitute n = 12, a = 15 and d = 1.5, we get
t12 = 1.5 + (12 – 1)1.5
= 1.5 + 11 × 1.5 = 1.5 + 16.5 = 18
Hence the 12th term of the sequence is 18.

Question 2.
Find the 21st term of the sequence, -2, -6, -10, -14, …
From the given sequence of A.P.
We have first term, a = -2
Common difference, d = -6 – (-2) = -6 + 2 = -4
∴ The nth term, tn = a + (n – 1)d
Substitute the value n = 21, a = -2 and d = -4, we get
t21 = -2 + (21 – 1) (-4)
= -2 + 20(-4) = -2 – 80 = -82

Question 3.
Find the 17th term of the sequence, 2x + 5x + 8x + 11x …
In the sequence of A.P.
Given the first term, a = 2x
Common difference, d = 5x – 2x = 3x
∴ The nth term, tn = ?
We know that, tn = a + (n – 1)d
Substitute the value n = 17, a = 2x, d = 3x in the above equation, we get
t17 = 2x + (17 – 1)3x
= 2x + 16 × 3x = 2x + 48x = 50x
Hence the 17th term is 50x.

Question 4.
Find the 11th term of the sequence, $$-\sqrt{2}$$ – $$3 \sqrt{2}$$ – $$5 \sqrt{2}$$ ………
In the sequence of A.P.
Given the first term, a = $$-\sqrt{2}$$
Common difference, d = – $$5 \sqrt{2}$$ – $$3 \sqrt{2}$$) = – $$5 \sqrt{2}$$ + $$3 \sqrt{2}$$ = –$$2 \sqrt{2}$$
The nth term, tn = ?
We know that, tn = a + (n – 1) d
When n = 11, a = $$-\sqrt{2}$$, d = -2$$\sqrt{2}$$, we have
t11 = $$-\sqrt{2}$$ + (11 – 1) (-2$$\sqrt{2}$$)
= –$$\sqrt{2}$$ +10 – 2$$\sqrt{2}$$) = $$-\sqrt{2}$$ – 20$$\sqrt{2}$$ =-21$$\sqrt{2}$$
Hence the 11th term is -21$$\sqrt{2}$$.

Question 5.
Find the 18th term of the sequence
(p – 9), (2p – q), (3p – 9), (4p – 9), …
The given sequence is in A.P.
Where, the first term, a = p – q
Common difference, d = (2p – q) – (p – q)
= 2p – q – p + q = p
The nth term, tn = ?
We know that, tn = a + (n – 1)d
Substitute the value n = 18, a = p – q, d = p, we get
t18 = (p – q) + (18 – 1)p
= p – q + 17p = 18p – q
Hence, the 18th term is (18 – q)

Question 6.
Find the 8th term of the A.P. 2, 5, 8, 11,…..
Given, a = 2, n = 8
The given sequence is an A.P.
The common difference d = 5 – 2 = 3
Therefore the nth term = a + (n – 1)d
i.e, tn = a+ (n – 1)d
tn = 2 + (8 – 1)3 = 2 + 7(3)
= 2 + 21 = 23

Question 7.
Find the sum of the series 99 + 101 + 103….. to 25 terms.
The given series is an A.P.
Hence, first term, a = 99 and common difference d = 101 – 99 = 2
∴ Then nth term,
tn = a + (n – 1)d
Putting n = 25, a = 99 and d = 2,
We get,
25th term, t25 = 99 + (25 – 1)2 = 99 + 48
= 147

Question 8.
Show that 13th and 50th terms of the series 25, 22, 19, 16, ….. are -11 and -122 respectively.
From the sequence, we have, a = 25, d = 22 – 25 = 3
The nth term, tn = a + (n – 1)d
When n = 13,
t13 = 25 + (13 – 1) (-3) = 25 + 12(-3) = 25 – 36
∴ t13 = -11 (shown)
Again, if n = 50, then
t50 = 25 + (50 – 1) (-3) = 25 + 49(-3) = 25 – 147
∴ t50 = -122 (shown)

Question 9.
The 12th term of an A.P exceeds the 3rd term by 36. If the 16th term is 64, determine the series.
Therefore, 12th term = a + 110 and 3rd term = a + 2d
Given, 12th term = 3rd term + 36 i.e., a + 110 = a + 2 + 36
⇒ 9d = 36 ∴ d = 4
Hence the series is
4, 4 + 4, 4 + 2(4), 4 + 3(4) …..
= 4,8, 4 + 8,4 + 12, …… i.e., 4, 8, 12, 16, …..

Question 10.
Find the sum of the sequence 5, 7, 13 to 20 terms.
The sequence of AP, where Ist term = 5
Common difference d = (7 – 5) = 2
given, n = 20
The sum of nth terms-
Sn = $$\frac{n}{2}$$[2a + (n – 1)d] = $$\frac{20}{2}$$[2 × 5 + (20 – 1)2]
= 10 (10 + (19 × 2)] = 10 [10 + 38] = 10 × 48 = 480
∴ Sum of the sequence is 480.

Question 11.
Is 132 a term of the series 6, 11, 16,……
The given series is an A.P.
Here, First term. a = 6
Common difference, d = 11 – 6 = 5
The nth term,
tn = a + (n – 1)d
⇒ 132 = 6 + (n – 1)5 ⇒ 132 = 6 + 5n – 5
⇒ 132 = 5n + 1 ⇒ 5n = 132 – 1 ⇒ n = $$\frac{131}{5}$$ ∴ n = 26.2
132 is not a term of the series 6, 11, 16

Question 12.
Which term of the series-10 – 5 + 0 + 5+ … is 25?
The given series is an A.P. Here, a = -10
d = -5 – (-10) = -5 + 10 = 5
nth term, tn = 25
Substituting the value of a, d and tn in the equation
tn = a + (n – 1)d
25 = -10 + (n – 1)5 ⇒ 25 = -10 + 5n – 5
⇒ 25 = -15 + 5n ⇒ 5n = 25 + 15
⇒ n = $$\frac{40}{5}$$ ∴ n = 8

Question 13.
Find the common difference of an A.P. where first term is 6 and 12th term is 72 also find the series.
Given, first term a = 6.
12th term, t12 = 72
Common difference, d = ?
The series is a, a + d, a + 2d …..
t12 = a + (n – 1)d
⇒ 72 = 6 + (12 – 1)d ⇒ 72 = 6 + 11d
⇒ 11d = 72 – 6 ⇒ d = $$\frac{66}{11}$$ ∴ d = 6
Hence the series 6, 12, 18, 24, 30,…

Question 14.
The three numbers are in the ratio 3 : 7 : 9. If 5 is subtracted from the second, the resulting numbers form an A.P. Find
the original numbers.
Let the numbers are 3x, 7x, 9x.
When 5 is subtracted from the second, 3x, 7x – 5, 9x.
We have, 7x – 5 = $$\frac{9 x+3 x}{2}$$
⇒ 7x – 5 = ⇒ 7x – 5 = 6x
⇒ 7x – 6x = 5 ∴ x = 5
Hence the original numbers are 3 × 5, 7 × 5, 9 × 5. i.e., 15, 35, 45.

Question 15.
Fill up the gaps of the following series in A.P. 20, -, -, -, 40.
Let ‘a’ be the first term and ‘ľ be the last term, a = 20
I = 40
The missing terms are a1, a2, a3.
We have, t5 = 40
But we know, tn = a + (n – 1)d
∴ t5 = a + 4d
⇒ 40 = 20 + 4d ⇒ 4d = 40 – 20 ⇒ d = $$\frac{20}{4}$$ ∴ d = 5
Hence the missing terms are 25, 30, 35.

Question 16.
Twenty persons are to be awarded prizes so that every person gets twice amount the previous person gets 2, what is the total amount spent on the prizes?
Consider, ‘a’ be the first term and ‘d’ be the common difference
Given, n = 20, a = 2, d = 2
:: Sn = $$\frac{n}{2}$$[2a + (n – 1) a s = $$\frac{20}{2}$$[2 × 2 + (20 – 1) 2s = 10(4 + 38) = 10(42) = 420
Hence, the total amount spent is 420.

Question 17.
A man saves 20 in the 1st month and 30 in the 2nd month and 40 in the 3rd month and so on. Find the total amount saved in 5 years.
We can express the amounts saved by the man in terms of A.P. where,
a = 20
d = 30 – 20 = 10
n = 12 × 5 = 60 months
We know that, sum of an A.P., sn = $$\frac{n}{2}$$[2a + (n – 1)]d
sn = $$\frac{60}{2}$$[2(20) + (60 – 1)10
= 30(40 + 590) = 30 × 630 = 18,900.
Hence, the total amount saved in 5 years is 18,900.

Question 18.
Find the sum of the series 72 + 70 + 68 +… + 40
a = 72, d = -2 l = 40
l = a + (n – 1)d
⇒ 40 = 72 + (n – 1) (-2) ⇒ 40 = 72 – 2n + 2
⇒ 2n = 34 ⇒ n = $$\frac{34}{2}$$ ∴ n = 17.
S = $$\frac{n}{2}$$ (a + l) = $$\frac{17}{2}$$(22 + 40) = $$\frac{17}{2}$$ (112) = $$\frac{1904}{2}$$ = 952

Question 19.
If a = -5, l = 52 and Sn = 470, Find n and d.
a = -5, l = 52, Sn = 470 n = ? d = ?
Sn = $$\frac{n(a+l)}{2}$$
⇒ 470 = $$\frac{n(-5+52)}{2}$$ ⇒ 470 = $$\frac{-5 n+52 n}{2}$$ ⇒ 470 = $$\frac{47 n}{2}$$
n = $$\frac{940}{47}$$ = 20 ∴ n = 20
Tn = a + (n – 1)d
⇒ 52 = -5 + (20 – 1)d ⇒ 52 = -5 + 19d ⇒ 57 = 19d ⇒ d = 3

Question 20.
Find the sum of all even integers from 72 to 768 both inclusive.
Terms of the series are 72, 74, 76,…768 .
tn = a + (n – 1)d
⇒ 768 = 72 + (n – 1)2 ⇒ 768 = 72 + 2n – 2
⇒ 768 = 2n + 70 ⇒ 2n = 768 – 70 ⇒ 2n = 698
n = $$\frac{698}{2}$$ = 349 S = $$\frac{n}{2}$$(a + l) = $$\frac{349}{2}$$ (72 + 768) = $$\frac{349}{2}$$ × 840
= 349 × 420 = 1,46,580

Question 21.
The last term of a series in AP is 40 and the sum of their series is 952. The common difference is -2. Find the first term and the number of terms in the series.
Given, l = 40, Sn = 952, d = -2
Consider,
Tn = a + (n – 1) (-2)
40 = 1 + (n – 1)(-2) or a – 2n + 2 = 40
= a – 2n = 38 i.e. a = 38 + 2n …………. (1)
Now,
s = $$\frac{n}{2}$$(a + 1) = 952 $$\frac{n}{2}$$ (a + 40) = 1904 = n(a + 40)
Now, substitute the value of a in above equation
1904 = n(38 + 2n + 40)
1904 = 38n + 2n2 + 40n
2n2 + 78n – 1904 = 0
or
n2 + 390 – 952 = 0
n2 + 56 – 17 – 952 = 0
n(n + 56) – 17 (n + 56) = 0
(n – 17) (n + 56) = 0
n + 56 = 0
= -56 Therefore it is impossible
n – 17 = 0
n = 17
∴ The last term is 17
a = 38 + 2 = 38 + 2 × 17 = 38 + 34
a = 72

Question 22.
Find the sumot all numbers between 200 and 550 are divisible 9.
The numbers between 200 and 550 which are divisible by 9 are 207, 213, 225, ………….. 549.
These numbers constitute a A.P.
Where, the first term, a = 207
common difference, d = 9
The number of term is obtained by
tn = a + (n – 1)d
549 = 207 + (n – 1)9
549 = 207 + 9n – 9
549 – 207 + 9n – 9
342 = 9n – 9
342 + 9 = 9n
351 = 9n
n = $$\frac{351}{9}$$ ∴ n = 39
Now, the sum of all numbers between 200 and 550 which are divisible by 6 can be obtained by
S = $$\frac{n}{2}$$(9 + d) = $$\frac{39}{2}$$ (207 + 549) = $$\frac{39}{2}$$ (756)
= 19.5 × 756 = 14,742

Question 23.
Find the sum of all the integers between 200 and 500 which are divisible by 5.
The number between 200 and 500 which are divisible by 5 are 205, 210, 215,… 495
These numbers constitute a AP
Where the Ist term, a = 205
Common difference, d = 5
nth term, Tn = 495
tn = a + (n – 1)d 495 = 205 + (n – 1)5
⇒ 495 – 205 = 5n – 5 ⇒ 290 + 5 = 5n ⇒ 5n = 295
n = $$\frac{259}{5}$$ n = 59
5 Now, the sum of all the numbers between 200 and 500 which are divisible by 5 can be obtain by
Sn = $$\frac{n}{2}$$(a+l) where l = last term
= $$\frac{59}{2}$$(205 + 495) = $$\frac{59}{2}$$ × 700 = 59 × 350 = 20,650

Question 24.
The sum of 3 numbers in A.P. is – 24 and their product is 288. Find the numbers.
Let the three numbers be a – d, a, a + d
∴ a – d + a + a + d = -24
⇒ 3a = -24 ⇒ a = $$\frac{-24}{3}$$ ∴ a = -8
(a – d) × a × (a + d) = 288
⇒ a(a2 – d2) = 288
⇒ -8[(-8)2 – d2) = 288 ⇒ -8[64 – d2] = 288
⇒ 8d2 – 512 = 288 = 8d2 = 288 + 512 = 800
⇒ d2 = $$\frac{800}{8}$$ = 100 = d2 = (10)2. d = 110
If d = 10, a = -8, the numbers are -18, -8, 2
If d = -10, a = -8, the numbers are 2, -8, -18

Question 25.
The sum of 3 numbers in AP is 9 and their product is 15. Find them.
Let the 3 numbers be:
A.P = a – d, a, a + d
The sum of 3 number is 9
= (a – d) + a + (a + d) = 9
3a – d + d = 9
3a = 9
a = 9/3
a = 3 ……….(1)
The product of 3 number is 15
(a – 3) (a) (a + d) = 15
(a2 – d2) (a) = 15 …..(2)
Now substitute the value of a=3 in above equation (2)
(32 – d2) (3) = 15
9 – d2 = $$\frac{15}{3}$$ = 5
d2 = 9 – 5 = 4
d = $$\sqrt{4}$$ = 2
Now substitute the value of a in equation …… (1)
a(1 + r + r2) = -21r
5(1 + r + r2) = -210r
5 + 5r + 5r2 = -21r
5r2 + 26r + 5 = 0
5r2 + 25r + r + 5 = 0
5r(r + 5) + 1(r + 5 ) = 0
(5r + 1) (r + 5) = 0
5r + 1 = 0 r + 5 = 0
5r = -1 r = -5
r = $$\frac{-1}{5}$$
When r = -5
The terms are = $$\frac{a}{r}$$, a, ar = $$\frac{5}{-5}$$, -5, 5x – 5
= -1, -5, -25
a = 3, d = 12
∴ A.P. = (a – d), a, (a + d)
= 3 – 2, 3, 3 + 2 = 1, 3, 5 or 5, 3, 1.

Question 26.
Which term of the following series is (18pet a) in the series (p + q) + (2p + q), (3p + q), …
The series is an A.P.
Where, the first term, a = p + q
Common difference, d = (2p + q) – (p + q) = 2p + q – p – q = p
The nth term, tn = 18p + q
We know that
tn = a + (n – 1)d
⇒ 18p + q = p + a + (n – 1)p (substitute the value)
⇒ q + np = 18p + q ⇒ np = 18p
⇒ n = $$\frac{18p}{p}$$ n = 18
Hence the 18th term of the sequence is (180 + 9).

Question 27.
If 3rd and 7th terms of an AP. are 15 and 39 respectively, find AP.
T3 = 15, T7 = 39
T3 = a + 2d, T7 = A + 6d a + d = 15
a + 2 × 6 = 15
a = 15 – 12 = 3
AP is a, a + d, a + 20, a + 3d……….
3, 3 + 6, 3 + 2(6), 3 + 3(6)……..
3, 9, 15, 21……..

Question 28.
If the 3rd and 6th terms of an A.P. are 7 and 13 respectively. 29 Find the A.P. and the 15th term.
T3 = 7, T6 = 13
T3 = a + 2d, T6 = a + 5d a + d = 7
a + 2(2) = 7
a + 4 = 7
a + 7 – 4
a = 3
∴ AP is
a, a + d, a + 2d, a + 3d, a + 4d, ………
3, 3 + 2, 3 + 2(2), 3 + 3(2), a + 4(2),…….
3, 5, 7, 9, 11, ………….
∴ T15 = a + 14d = 3 + 14(2) = 3 + 28 = 31

Question 29.
The sum of 4th and 11th term of an A.P. is 75 and the sum of 6th and 14th term is 105. Find the 30th term
Let, ‘a’ be the first term and ‘d’ be the common difference and a, a + d, a + 20, …… be the series of A.P.
∴ t4 = a + 3d and T11 = a + 10d
t6 = a + 5d and T14 = a + 13d
Given, t4 + t11 = 75
i.e., a + 3d + a + 10d = 75 ⇒ 2a + 13d = 75 …… (1)
and T6 + T14 = 105
i.e., a + 5d + a + 13d = 105 ⇒ 2a + 180 = 105 …. (2)
Subtracting (1) from (?), we get
5d = 30 ∴ d = 6
Substitute, d = 6 in. (1), we get
2a = 75 – 13 × 6
⇒ 2a = 75 – 78 ∴ a = $$\frac{-3}{2}$$
30th term, T30 = a + (30 – 1)d = $$\frac{-3}{2}$$ + 29 × 6 = $$\frac{-3+348}{2}$$ = $$\frac{345}{2}$$ = 172$$\frac{1}{2}$$
∴ The 30th term is 172$$\frac{1}{2}$$.

Question 30.
A man is employed to count 10,710. He counts at the rate of 180 per minute for half an hour. After this, he counts at the rate of 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
A man counts 180 in 1 minute.
Therefore he will count (180 × 30) = 5400 in 30 minutes,
The balance amount left is 10710 – 5400 = 5310
According to the given data he counts. 3 less every minute than the preceding minute. Therefore it forms an arithmetic progression which is as follows:
177, 174, 171,………..
The sum of this A.P. is 5310
Therefore,
5310 = $$\frac{n}{2}$$[(2a + (n – 1)d)]
Where d = -3, a = 177
= $$\frac{n}{2}$$[(354 + (n-1)(-3)]
n = 12
Therefore total time taken = 30 + n = 42 minutes.

Question 31.
How many terms of the series 35, 31, 27, must be taken so that the sum may be 105.
Given a = 35, d = 31 – 35 = -4, s = 105
We know, Sum, S = $$\frac{n}{2}$$(2a + (n – 1)d]
Substituting for a, d and s, we get
105 = $$\frac{n}{2}$$[2 × 35 + (n – 1)(-4)]
= 105 = $$\frac{n}{2}$$(70 – 4n + 4)
⇒ 105 = $$\frac{n}{2}$$(70 – 4n + 4) ⇒ 105 = $$\frac{n}{2}$$(74 – 4n)
⇒ 105 = n(37 – 2n) ⇒ 105 = 3n – 2n2
⇒ 2n2 – 37n + 105 = 0 ⇒ 2n2 – 30n – 7n + 105 = 0
⇒ 2n(n – 15) – 7(n – 15) = 0 ⇒ (n – 15) (2n – 7) = 0
n = 15 or 2n = 7
n = 15 or n = $$\frac{7}{2}$$ But n = $$\frac{7}{2}$$ iş impossible.
Hence the number of terms is 15.

Question 32.
Find the sum of all numbers between 300 and 650 which are divisible by 6.
The numbers between 300 and 650 which are divisible by 6 are 300, 306, 312, 318, ….., 648.
These numbers constitute a A.P.
Where, the first term, a = 300
Common difference, d = 6
nth term, tn = 648
The number of terms is obtained by
tn = a + (n – 1)d
⇒ 648 = 300 + (n – 1)6
⇒ (n – 1)6 = 348 ⇒ n – 1 = $$\frac{348}{6}$$ ⇒ n – 1 = 58
⇒ n = 58 + 1 ∴ n = 59
Now, the sum of all numbers between 300 and 650 which are divisible by 6 can be obtained by
S = $$\frac{n}{2}$$(a + l) = $$\frac{59}{2}$$(300 + 648) = $$\frac{59}{2}$$ × 948 = 27,966

Question 33.
Find the sum of all integers between 100 and 400 which are divisible by 7 (seven).
a = 105, an = 399, d = 7
an = a + (n – 1)d
399 = 105 + (n – 1)7
399 = 105 + 7n – 7
301 = 7n
n = 43
Sn = $$\frac{n}{2}$$(a + 1)
Sn = $$\frac{43}{2}$$(105 + 399) = $$\frac{43(504)}{2}$$ = 10836

Question 34.
A class consists of member of boys whose ages are in AP. The common difference being 4 months.
If the youngest boy of the class be only 8 years old and the sum of all the ages of all the boys in the class be 168. Find the number of boys.
d = 4 months = 6/12 = 0.33 years, a = 8 years, Sn = 168
Sn = $$\frac{n}{2}$$[2a+ (n − 1)d]
168 = $$\frac{n}{2}$$(2a + (n − 1)d]
336 = n(16 + 0.33n – 0.33]
336 = 15.670 + 0.33n2
0.33n2 + 15.67n – 336 = 0
On simplifying
n = 16 and n = -63.51
(negleting this value as n cannot be -ve)

Problems on Geometric Progression

Question 35.
The 4th and 8th terms of a G.P. are 24 and 384 respectively. Sind the 5th term.
Tn = arn-1
ar4-1 = 24 ⇒ ar3 = 24 ………(i)
ar8-1 = 384 ⇒ ar7 = 384 ……… (ii)
Dividing equation (ii) by (i) we get
$$\frac{a r^{7}}{a r^{3}}$$ = $$\frac{384}{24}$$ ⇒ r4 = 16 ⇒ r4 = 24
∴ r = 2
P = 2 Put r = 2 in equation (1)
2. (2)3 = 24 ⇒ a8 = 24 ⇒ = $$\frac{24}{8}$$ = 3
5th term = a$$\left(\frac{r^{n}-1}{r-1}\right)$$ = 3$$\left(\frac{2^{5}-1}{2-1}\right)$$ = 3$$\left(\frac{32-1}{2-1}\right)$$ = 3$$\left(\frac{31}{1}\right)$$ = 31 × 31 = 93

Question 36.
The sum of 3 numbers in GP is -21 and their product is 125. Find them.
Let the 3 numbers of G.P. be = $$\frac{9}{r}$$, a, ar
The sum of 3 numbers is -21
$$\frac{9}{r}$$ + a + ar = -21
a(1 + r + r2) = -21r ……………….(1)
The product of 3 numbers is 125
= $$\frac{a}{r}$$ × a × ar = 125 = a3 = 125
= $$\frac{a}{r}$$ = $$\sqrt{125}$$ = 5
when r = $$\frac{-1}{5}$$, a = -5
= 25, -5

Question 37.
The sum of 3 terms in G.P. is 14 and their product is 64. Find them.
Let the 3 numbers of G.P. be $$\frac{9}{r}$$, a, ar
The sum of 3 numbers is 14
$$\frac{9}{r}$$ + a + ar
a(1 + r + r2) = 14r
The product of 3 number is 64
⇒ $$\frac{a}{r}$$ + a + ar = 64 ⇒ a3 = 64 ⇒ a = 4
When r = $$\frac{1}{4}$$, a = 4 = 16, 4

Question 38.
The sum of three numbers in G.P is 28 and their product is 512. Find the numbers.
Let, the three numbers be, $$\frac{a}{r}$$, a, ar
Given the sum = 28
⇒ a|$$\frac{1}{r}$$ + 1 + r2| = 28 = a(1 + 1 + r) = 28r …. (1)
and the product = 512
i.e. $$\frac{a}{r}$$ × a × ar = 512 ⇒ a3 = 512 ⇒ a3 = (8)3
∴ a = 8
Substitute, a = 8 in (1), we get
8(1 + 1 + r2) = 28r
⇒ 8 + 8 + 8r2 – 28r = 0 ⇒ 8r2 – 20r + 8 = 0
⇒ 2r2 – 5r + 2 = 0 ⇒ 2r2 – 4r – r + 2 = 0
⇒ 2r(r – 2) – 1(r – 2) = 0 ⇒ (r – 2) (2r – 1) = 0
r = 2 or 2r = 1 r = $$\frac{1}{2}$$
When r = 2, the terms are $$\frac{8}{2}$$, 8, 8 x 2 i.e., 4, 8, 16
when r = $$\frac{1}{2}$$, the terms are $$\frac{8}{\frac{1}{2}}$$, 8 × $$\frac{1}{2}$$ ie., 16, 8, 4

Question 39.
The sum of three numbers in a’GP is 14 and their product is 64. Find the numbers by using formula.
Given, the product = 64.
$$\frac{a}{r}$$ × a × ar = 64
⇒ a3 = 64 ⇒ a3 = 43 ∴ a = 4
and, the sum = 14 ∴ $$\frac{a}{r}$$ + a + ar = 14
⇒ $$\frac{a}{r}$$ + 4 + 4r = 14 ⇒ $$\frac{4+4 r+4 r^{2}}{r}$$ = 14
⇒ 4 + 4r + 4r2 = 14r ⇒ 4r2 + 4r – 14r + 4 = 0
⇒ 4r2 – 10r + 4 = 0 ⇒ 2r2 – 5r + 2 = 0
⇒ 2r2 – 4r – r + 2 = 0 ⇒ 2r(r – 2) – 1(r – 2) = 0
⇒ (r – 2)(2r – 1) = 0
Now r – 2 = 0 2r – 1 = 0
∴ r – 2 ⇒ 2r = 1
∴ r = 1/2
The number are : 1) When a = 4, r = 1/2
then a/r, a, ar = 4/1/2, 4, 4 × 1/2 = 8,4,2
2) When a = 4, r = 2 then a/r, a, ar = 4/2 4, 4.2 = 2,4,8

Question 1.
What is Interest?
The reward which is paid for the use of capital is called interest. That is, it is ange paid by the borrower to the lender for the use of barrowed money. The borrower is called the debtor and the lender is called the creditor.

Question 2.
Define Simple Interest.
Simple interest is the interest produced by the principal alone. i.e., interest calculated only on the original principal is known as simple interest. Three factors – the principle, the rate of interest and the term of loan is considered to calculate simple interest.

Question 3.
Define compound Interest
Compound interest is obtained when the interest at the end of fixed period is added to the principal and the amount is taken as the principal of the next period.

Question 4.
What is Rate of Interest?
For a given time, the interest paid for the use of a certain sum, which is borrowed, from other person is called the rate of interest. In general, the interest paid per hundred per year is known as the rate of interest. i.e., the interest on ₹ 100 for one year is generally taken as the rate of interest.

Question 5.
What is banker’s discount?
Banker’s Discount is the simple interest calculated by the banker on the Face Value of the bill.
B.D = F × t × r Where, F = Face Value, t = Discount period (time) r = rate, of interest (discount rate)

Question 6.
What is Banker’s gain?
The difference between banker’s discount and true discount is called the banker’s gain. While banker’s discount is charged on the face value; true discount is calculated on the true present worth. Banker’s discount is always greater than true discount.

Question 7.
What is annuity?
An annuity is a fixed sum of money payable periodically at equal interval of time under certain conditions such as pention, interest, LIC premium etc.

Question 8.
State the various types of annuities.
The various types of annuities are as follows:

1. Annuity certain: An agreement to make a fixed number of annuity payments of the beginning or at the end of the period.
2. Annuity contingent: Amount payable on the happening of an event.
3. Deferred annuity: Under this, payments begin only after a lapse of fixed period.
4. Annuity immediate: Where annuities are payable at the end of each stipulated · period.
5. Annuity due: Where annuity payments are payable at the beginning of each stipulated time period.

Question 9.
Define Ratio.
The ratio is the relation in which one quantity is compared to another quantity of the same kind with regard to their magnitudes by considering what multiple, the first quantity is of second and part to parts.

Question 10.
What do you mean by present value of a bill?
Present value of a bill is the difference between the Face value and discount charged and deducted by the banker.
Present value of a bill = Face value – Banker’s discount.

Question 11.
What is a bill of exchange?
A bill of exchange is an instrument in writing, containing an unconditional order, signed by the maker, directing a certain person, to pay a certain sum of money only to, or to the order of ascertain person, or to the bearer of the instrument.

Question 12.
What is common ratio?
A Ratio is the relationship between two quantities of the same kind, with respect to their magnitude and denotes how many times one of the quantities is contained in the other.

Question 13.
What is a duplicate ratio? Give an example,
When a ratio is compounded by itself, the resultant ratio is called duplicate ratio.
Example: Duplicate ratio of a : b is a2 : b2

Question 14.
State the difference between common ratio and common difference.
Common difference is the difference between, the two consequent terms of an A.P. where som mammoint eretice is the ratierercen between whereas, common ratio is the ratio of the consequent terms of the G.P.

Question 15.
State the difference between ratio and proportion.
The difference between Ratio and proportion are

1. There are two terms in a ratio, there are 4 term in a proportion. .
2. Ratio is a comparision of two quantities of the same kind, proportion is a comparision of two ratios.

Question 16.
What do you mean by Proportion?
Proportion is the fact that one ratio is equal to another ratio, that can be write ratio a : be equal to ratio c : d.
Example. To show that the ratio of 2 to 5 is equal to ratio of 4 to 10. The form of proportion 2 : 5 :: 4 : 10

Question 17.
What is Direct Proportion?
When an increase (or decrease) in one kind of quantities is accompanied by an increase (or decrease) in another quantity, is called direct proportion.

Question 18.
What do you mean by Inverse Proportion?
When an increase (or decrease) of one kind of quantity is accompanied by a decrease (or increase) in another is known as Inverse Proportion.

Question 19.
What do you mean by Continued Proportion?
Quantities such that the first is to the second, as the second is to the third, as the third is to the fourth and so on are said to be as continued proportion.

Problems for 2 Marks

Question 1.
In what time will ₹ 1,250 amount to ₹ 2,150 at 9% p.a. simple interest?
Here, P = 1,250, A = 2,150, R = 9%, SI = (2,150 – 1,250) = 900
T = $$\frac{\text { ST } \times 100}{\text { PR }}$$ = $$\frac{900 \times 100}{1250 \times 9}$$ = 8 years

Question 2.
In what time will a sum of 2,000 amounts to ₹ 240 at the rate of 4% p.a. simple interest?
T = $$\frac{S T \times 100}{P \times R}$$ = $$\frac{240 \times 100}{2000 \times 4}$$ = 3 years

Question 3.
In what period will 3 750 amount to ₹ 975 at 5% p.a. simple interest?
P = 750, A = 975, R = 5%, SI = 975 – 750 = 225, T = ?
T = $$\frac{S I \times 100}{P \times R}$$ = $$\frac{225 \times 100}{750 \times 5}$$ = 6 years

Question 4.
At what rate of simple interest will ₹ 750 amount to ₹ 815 in 11 months?
Given P = ₹ 750, A = ₹ 815
∴ SI = A – p = 815 – 750 = ₹ 65
T = $$\frac{11}{12}$$ years
∴ Rate, R = $$\frac{\mathrm{SI} \times 100}{\mathrm{P} \times \mathrm{I}}$$ = $$\frac{65 \times 100}{750 \times \frac{11}{12}}$$ = $$\frac{65 \times 100 \times 12}{750 \times 11}$$ = 9.45%

Question 5.
How much interest will be earned on 3 2,000 at 8.5 simple interest in 2 years.
S.I = $$\frac{\text { PTR }}{100}$$ = $$\frac{2,000 \times 2 \times 8.5}{100}$$ = ₹ 340

Question 6.
At what rate percent per annum simple interest will a sum of money double itself in 10 years?
Let, the principal be 100; Amount in 10 years is ₹ 200
R = $$\frac{S I \times 100}{P \times T}$$ = $$\frac{100 \times 100}{100 \times 10}$$ = 10%

Question 7.
Find the simple interest on ₹ 2,276 for 2 years 6 months at 12.5% p.a.
Given, p = 2,276, R = 12.5% T = 2 years 6 months = 2.5 years.
SI = $$\frac{P \times R \times T}{100}$$ = $$\frac{2,276 \times 12.5 \times 2.5}{100}$$ = $$\frac{71,125}{100}$$ = ₹ 711.25

Question 8.
Find the simple interest on ₹ 14,530 for 4 years at the rate of 8$$\frac{1}{2}$$% p.a.
SI = $$\frac{P R T}{100}$$
Here, P = 14,530, R = 8$$\frac{1}{2}$$% = $$\frac{17}{2}$$%p.a. ; T = 4 years
= $$\frac{14,530 \times \frac{17}{2} \times 4}{100}$$ = $$\frac{14,530 \times 17 \times 4}{100 \times 2}$$ = $$\frac{9,88,040}{200}$$ = ₹ 4,940.20

Question 9.
Find the simple interest on ₹ 600 for 3 years at 4% p.a. What is the amount after 3 years.
Given, P = ₹ 600, R = 4% p.a. T = 3 years
SI = $$\frac{\text { PRT }}{100}$$ = $$\frac{600 \times 4 \times 3}{100}$$ = $$\frac{7,200}{100}$$ = ₹ 72
Amount, A = P + SI = 600 + 72 = ₹ 672

Question 10.
If simple interest on a certain sum is ₹ 360 for 2 years @ 6% p.a. find the sum.
Given, P = ₹ 360 R = 6% p.a., t = 2 years
SI = $$\frac{P \times R \times T}{100}$$ 360 = $$\frac{P \times 6 \times 2}{100}$$ 36000 = 12P
P = $$\frac{36000}{12}$$ P = 3000 ∴ The sum is ₹ 3000

Question 11.
Find compound interest on ₹ 2,560 for 3 years at 8% p.a.
Given p = 2,560, R = 8%, T = 3 years
CI = $$\left(1+\frac{R}{100}\right)^{\top}$$ – P
= 2,560$$\left(1+\frac{8}{100}\right)^{3}$$ -2,560 = 2,560 × 1.26 – 2,560 = 665.6

Question 12.
In what time will a sum of ₹ 4,000 amounts to ₹ 4,480 at the rate of 5% p.a. simple interest?
Given, P = ₹ 4,000; A = ₹ 4,480, SI = ₹ 4,480 – 4,000 = 480, R = 5%, T = ?
T = $$\frac{S I \times 100}{P \times R}$$ = $$\frac{480 \times 100}{4,000 \times 5}$$ = 2.4 years

Question 13.
Find the compound interest on ₹ 12,000 at 8% p.a. for 4 years.
Given, P = ₹ 12,000, R = 8%, T = 4.
Compound Interest, CI = P $$\left(1+\frac{\mathrm{R}}{100}\right)^{\top}$$ – P = 12,000$$\left(1+\frac{8}{100}\right)^{4}$$ – 12,000
= 12,000(1 + .08)4 – 12,000 = 12,000 × 1.36 – 12,000
= 16,325.86 – 12,000 = 4,325.86 (₹)

Question 14.
Find the compound interest on ₹ 3,000 for 3 years at 4% p.a.
CT = P $$\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{T}}$$
3000 (1.04)3 = 3000 ( 1.12486) = 3374.60
∴ Compound interest 3374.60

Question 15.
By selling an article for ₹ 121 a dealer gains 10%. What is the percentage of profit or loss if he has sold the article for 104.50?
Let x be the cost price of the article
Then,
Selling price = Cost Price + Gains
⇒ 121 = x + x10% ⇒ 121 = x + 0.1x
⇒ 121 = 1.1x ⇒ x = $$\frac{121}{1.1}$$ x = 110; The cost Price = ₹ 110
When the article is sold for ₹ 104.50
Profit or loss = 104.50 – 110
Loss = -5.5
The dealer losses by 5% ($$\frac{-5.5}{110}$$ × 100).

Question 16.
In what time will ₹ 5,000 amount to ₹ 5618 at 6% compound interest?
Given, P = ₹ 5,000 ; A = ₹ 5,618 ; R = 6; T = ?
We know, A = P$$\left(1+\frac{R}{100}\right)^{\top}$$
⇒ $$\frac{A}{P}$$= $$\left(1+\frac{R}{100}\right)^{\top}$$ ⇒ $$\frac{5,618}{5,000}$$ = $$\left(1+\frac{6}{100}\right)^{\top}$$ ⇒ $$\frac{2,809}{2,500}$$ = $$\left(\frac{106}{100}\right)^{\top}$$
$$\left(\frac{53}{50}\right)^{2}$$ – $$\left(\frac{53}{50}\right)^{\top}$$ ∴ T = 2 years

Question 17.
Find the compound interest on ₹ 2,500 for 2 years at 12% p.a.
Given, P = ₹,500, R = 12% T = 2 years.
CI = P$$\left(1+\frac{R}{100}\right)^{\top}$$ – P
= 2,500$$\left(1+\frac{12}{100}\right)^{2}$$ – 2,500 = (2,500 × 1.25) – 2,500
= 3,125 – 2,500 = 625

Question 18.
By selling article for ₹ 530, a person loses 15%. To gain 10% what must be the price?
Given, the selling price = ₹ 530, Loss = 15%
∴ Cost price = $$\frac{100}{85}$$ × 530 = 623.52 (₹)
To gain 10%, the selling price
= $$\frac{110}{100}$$ × 623.52 = 685.87 (₹)

Question 19.
Calculate the amount of an annuity of ₹ 5,000 for 15 years, at 12% . p.a. interest.
Nothing is mentioned about the type of annuity. Therefore, it should be taken as Annuity Immediate.
Given annuity (A) = ₹ 5,000, n = 15 years and r = 0.12 F = ₹ 1,49,006.97
(1.12)15 = A.1 (15 log 1.2)
= A.1 (15 × 0.0492)
= A.1(0.7380) = 5.4702

Question 20.
A sum of money invested at a compound interest amounts to ₹ 10,816 at the end of second year and ₹ 11,248.64 at the end of 3rd year.
Find the rate of compound interest and the sum.
A = P(1 + i)n
Where A = amount, P = principal, i = Rate of interest n = time
As given,
11248.64 = P(1 + i)3 …………… (i)
10816 = P(1 + i)2 ……………… (ii)
Dividing (i) by (ii)
$$\frac{11248.64}{10816}$$ = $$\frac{P(1+i)^{3}}{P(1+i)^{2}}$$
⇒ 1.04 = (1 + i) ⇒ 1.04 – 1 = i ⇒ 1 = .04 ∴ 1 = 4%
Rate of interest = 4%
∴ 10816 = P(1.04)2 ⇒ p = $$\frac{10816}{1.0816}$$
= 10,000 Principal = 10,000

Question 21.
If 36 men can do a piece of work in 25 days, in how many days, will 15 men do it?
Given, $$\frac{36}{15}$$ = $$\frac{x}{25}$$
15x = 36 × 25
15x = 900
x = 60
15 men will take 60 days to complete the work.

Question 22.
16 men or 28 women can do a work in 40 days. In how many days will 24 men and 14 women complete the same work?
16 Men = 28 Women
⇒ 1 Man = $$\frac{28}{16}$$ Women = 1.75 Women x = $$\frac{28 \times 40}{56}$$ = 20 days

Question 23.
A number is divided into 3 parts in the ratio of 2 : 3 : 4. If the second part is 81. Find the other numbers.
Let the Nos. be a – d, a & a + e
Here a = 81
Ratio between Ist & 2nd numbers = 2 : 3
∴ $$\frac{a-d}{a}=\frac{2}{3}$$ $$\frac{81-d}{81}=\frac{2}{3}$$
d = 27 ∴ Ist No. 81 – 27 = 54
Now ratio of 2nd and 3rd No = 3 : 4
$$\frac{a}{a+e}$$ = $$\frac{3}{4}$$
$$\frac{81}{81+e}$$ = $$\frac{3}{4}$$
e = 27 3rd No. = 81 + 27 = 108.

Question 24.
Express the lowest terms the ratio of $$\frac{5}{12}$$ of $$\frac{7}{18}$$
Given, $$\frac{5}{12}$$ : $$\frac{7}{18}$$
Lowest term = $$\frac{5}{12} \times \frac{18}{7}$$ = $$\frac{15}{14}$$
Lowest terms is 15 : 14

Question 25.
Write the inverse ratio of $$\frac{7}{2}$$ to $$\frac{9}{4}$$ and reduce it to its lowest terms.
Given $$\frac{7}{2}$$ : $$\frac{9}{4}$$
Inverse of ratio is $$\frac{9}{4}$$ : $$\frac{7}{2}$$
Lowest terms $$\frac{9}{4}$$ ÷ $$\frac{7}{2}$$
Lowest terms are $$\frac{9}{4}$$ × $$\frac{2}{7}$$ = $$\frac{9}{14}$$

Question 26.
If 6 taps can fill a tank in 4 hours. How many taps are required to fill the same tank in 12 hours?
In 4 hrs. number of taps required to fill the tank = 6
In 1 hr. number of taps required to fill the tank = 6 × 4
Therefore in 12 hours number of taps required to fill the tank = $$\frac{6 \times 4}{12}$$ = 2

Question 27.
Divide ₹ 35 between two men in the ratio of 3 : 4.
Given the ratio 3 : 4
Sum of the ratio = 3 + 4 = 7
First man gets $$\frac{3}{7}$$ of 35 = ₹ 15
Second man gets = $$\frac{4}{7}$$ of 35 = ₹ 20

Question 28.
P’s income is ₹ 280 and is increased by ₹ 35, If Q’s salary which is ₹ 256 increased in the same ratio. Find Q’s increased salary.
p’s income increases by ₹ 35
i.e., P’s income increase is $$\frac{1}{8}$$ of the salary
So, $$\frac{1}{8}$$ of the salary of Q = $$\frac{256}{8}$$ = 32
∴ B’s salary increase by ₹ 32

Question 29.
The income of A and B is in the ratio of 4 : 3 and their expenditure is in the ratio of 3 : 2.
If both of them save ₹ 6,000 at the end of each month find their respective monthly income.
Let the income be x
Let the expenditure be y
Ratios of the income of A and B = 4x : 3x
Ratio of the expenditure of A and B = 3y : 2y
Saving of both A and B are 6,000
Savings = Income – Expenditure
6,000 = 4x – 3y
6,000 = 3x – 2y
Solving the equastions simultaneously we get,
4x – 3y = 6,000 × 3
3x – 2y = 6,000 × 4 y = $$\frac{6,000}{5}$$ = 1,200
4x – 3(1,200) = 6,000
4x – 3,600 = 6,000
x = $$\frac{9,600}{4}$$ = 1,600
Therefore the Income of A = 4x = 4(1,600) = 6,400
Income of B = 3x = 3(1,600) = 4,800

Question 30.
Find out the 3$$\frac{1}{4}$$% of ₹846.
3$$\frac{1}{4}$$% of ₹846 = 34 = $$\frac{846 \times 3.25}{100}$$ = ₹ 27.495

Question 31.
Two numbers are in the ratio of 7 : 3. Their difference is 20. Find the\frac{846 \times 3.25}{100}numbers.
Let the number be 7x and 3x
There difference 7x – 3x = 20
⇒ 4x = 20
∴ x = 5
Hence, the required number are 7x = 7 (5) = 35
3x = 3(5) = 15

Question 32.
lf x : 3 = 50 : 2. Find x.
x : 3 = 50 : 2
2x = 150
x = $$\frac{150}{2}$$ ∴ x = 75

Question 33.
Two numbers are in the ratio 5:8. If the sum of the numbers in 182. Find the number,
Let, the number are 5x and 8x
5x + 8x = 182
⇒ 13x = 182 ⇒ x = $$\frac{182}{13}$$
∴ x = 14
So, numbers are 5 × 14 = 70 and 8 × 14 = 112

Question 34.
Find the fourth proportional to 6,8 and 9.
Let the fourth proportional is x
So 6 : 8 = 9 : x
⇒ $$\frac{6}{8}=\frac{9}{x}$$ ⇒ 6x = 72 ⇒ x = $$\frac{72}{6}$$ = 12 ∴ x = 12
∴ The fourth proportional is 12.

Question 35.
Find the third proportional to 3 : 9.
Let, the third proportional be x
3 : 9 : x are in the third proportion.
92 = 3x ; 3x = 81
∴ x = 27 ∴ 27 is the third proportional to 3 : 9 : 27

Question 36.
Find the third proportional of 4 and 8.
Let, the third proporation be x
4 : 8 : x are in the third proportion
82 = 4x ⇒ 4x = 64 ⇒ x = $$\frac{64}{4}$$ ⇒ x = 16
∴ 16 is the third proportional to 4 : 8 : 16

Problems on Simple and Compound Interest

Question 1.
Find the simple interest at 6% p.a. on a principal amount of ₹ 1500 for 6 months and 10 days.
Given P = ₹ 1,500 ; R = 6% ; T = 6 months, 10 days
= 6 + $$\frac{10}{30}$$ months = $$\frac{19}{3} \times \frac{1}{12}$$ = $$\frac{19}{36}$$ years
We know that, SI = $$\frac{\text { PRT }}{100}$$ = $$\frac{1,500 \times 6 \times \frac{19}{36}}{100}$$ = 15 × 6 × $$\frac{19}{36}$$ = 47.5
∴ The simple interest is ₹ 47.5

Question 2.
A sum of money amounts to ₹ 855 in 3 1/2 years ar the rate . of 4% p.a. simple interest. Find the sum.
Given, 855 = P + PRT
855 = P$$\left(1+3.5 \times \frac{4}{100}\right)$$ 855 = P$$\left(1+\frac{14}{100}\right)$$ P = $$\frac{855 \times 100}{114}$$ = ₹ 750

Question 3.
In 12 years a sum of money becomes double. In how many years will it triple itself ?
Let, the principal be ₹100
Amount = ₹ 200 (double of principal)
∴ SI = 200 – 100 = ₹ 100
Given, Time T = 12 years
∴ Rate = $$\frac{\mathrm{SI} \times 100}{\mathrm{P} \times \mathrm{T}}$$ = $$\frac{100 \times 100}{100 \times 12}$$ = $$\frac{100}{12}$$ = $$8 \frac{1}{3}$$%
To triple the sum, Amount = 3 × 100 = 300 (Rs)
∴ SI = 300 – 100 = ₹ 200 R = $$\frac{25}{3}$$%
Time = $$\frac{S I \times 100}{P \times R}$$ = $$\frac{200 \times 100}{100 \times \frac{25}{3}}$$ = $$\frac{200 \times 3}{25}$$ = 24 years

Question 4.
Mr. Arun gets a certain sum of money as prize in a lottery and deposited the same in a bank. It amounted to ₹ 1,624 in 4 years and amounts to ₹ 1,736 in 6 years. Find the prize amount and the rate of simple interest allowed by the bank..
Amount in 6 years — 1,736
Amount in 4 years — 1,624
Difference SI for 2 year — 112
S.I for 4 years 112 × 2 = 224
P = A – S.I = 1,624 – 224 = 1,400
Rate = $$\frac{\mathrm{SI} \times 100}{\mathrm{P} \times \mathrm{n}}$$ = $$\frac{224 \times 100}{1,400 \times 4}$$ = 4%

Question 5.
M borrowed ₹ 12,650 from a money lender at 18% p.a. simple interest. After 3 years, he paid rs. 10,381 and gave a buffalo to clear off the debt. What is the cost of the buffalo?
Given P = ₹ 12,650, R = 18% T = 3 years.
Simple interest
SI = PRT = 12,650 × 18% × 3 = 37,950 × $$\frac{18}{100}$$ = 6,831
Let, Bufflo’s cost = ‘X’
10,381 + x = 12,650 + 6,831 ⇒ x = 19,481 – 10,381
∴ x = 9,100 Hence, Buffalo cost ₹ 9,100

Question 6.
A person invests ₹ 1200 for 4 years and ₹ 1500 for 3 years. The rate of simple interest being the same in both the cases.
Find the rate of interest if he receives ₹ 450 altogether.
Let, the interest on ₹ 1,200 for 4 years is ‘a’.
So, the interest on ₹ 1,500 for 3 years = ₹ (450 – a)
When, P = ₹ 1,200 ; T = 4 years ; SI = a ∴ The rate of interest is 4.83%.

Question 7.
A man deposits 5,000 in a savings account which pays a simple interest at a rate of 4.5% for the first two years and then at the rate of 5% for the next three years. Find the amount due at the end of five years.
Here, for the first two years
Principle amount, P = ₹ 5,000, Time period, T = 2
Rate of interest, R = 4.5% (0.045) ∴ The amount due at the end of five years is 5,000 + 450 + 750 = ₹ 6,200

Question 8.
Find the compound interest on ₹ 13,500 at 7% p.a. for 6 years.
Given, Principal, p = ₹ 13,500, Rate, R = 7% Time, T = 6 years
We know that,
Compound interest CI = $$\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{T}}$$ – P
= 13,500 $$\left(1+\frac{7}{100}\right)^{6}$$ – 13,500 = 13,500(1.07)6 – 13,500
= 13,500 × 1.5007 – 13,500 = 20259.85 – 13,500
= ₹ 6759.85
Hence, the compound interest = ₹ 6759.85

Question 9.
Calculate the amount and interst on ₹ 100 for 20 years allowing the compound interest at 5% p.a.
P = Rs. 100, n = 20 years, r = 5%, A = ? CI = ?
A = P$$\left(1+\frac{r}{100}\right)^{r}$$ – 100$$\left(1+\frac{5}{100}\right)^{20}$$ = 100 (2.6532 = ₹ 265.329
CI – A – P = 265.329 – 100 = ₹ 165.329

Question 10.
What would be the amount of compound interest (CI) on ₹ 5,000 at 5% rate of interest p.a. for 3 years?
P = 5,000 R = 5% T = 3 years
CI =P $$\left(1+\frac{R}{100}\right)^{\top}$$ – P
= 5,000$$\left[1+\frac{5}{100}\right]^{3}$$ – 5,000
= 5,000 (1.05)3 – 5,000 = 5,788.12 – 5,000 = ₹ 788

Question 11.
Find the compound interest on ₹ 20,000 at 6% p.a. for 4 years. What is the simple interest on the same amount.
P = 20,000 R = 6% T = 4
CI = P$$\left[1+\frac{\mathrm{R}}{100}\right]^{\mathrm{T}}$$ – P
= 20,000$$\left(1+\frac{6}{100}\right)^{4}$$ – 20,000 = 20,000 (1.06)4 – 20,000
= 20,000 × 1.2625 – 20,000 = 25, 242.54 – 20,000 = ₹ 5249.54
SI = $$\frac{\text { PTR }}{100}$$ = $$\frac{20,000 \times 4 \times 6}{100}$$ = ₹ 4,800

Question 12.
Find the difference between the simple interest and compound interest on ₹ 8,550 at 6% in 4 years.
Given, Principal, P = ₹ 8,550, Rate, R = 6%, Time, T = 4 years
∴ Simple interest, SI = $$\frac{\text { PRT }}{100}$$ = $$\frac{8,550 \times 6 \times 4}{100}$$ = ₹ 2,052
Compound interest, CI = P$$\left(1+\frac{R}{100}\right)^{\top}$$ – P
= 8,550$$\left(1+\frac{6}{100}\right)^{4}$$4 – 8,550 = 8,550(1.06)4 – 8,550
∴ The difference between ci and SI = ₹ 2,244.18 – ₹ 2,052 = ₹ 192.18

Question 13.
Find the difference between the S.I. and C.I on ₹ 3,000 in 3 years at 4% p.a
Find 3 years at 4% p.a ,
SI = $$\frac{\text { PTR }}{100}$$ = $$\frac{3000 \times 3 \times 4}{100}$$ = 360 CI = P$$[\left(1+\frac{R}{100}\right)^{\top}$$ – P
3000(1 + 4)3 – 3000 = 3000 (1.12486) – 3000 = 3374.60 – 3000
CI = 374.60
Difference between CI and SI = 374.60 – 360 = 14.60

Question 14.
The difference between SI and CI on certain sum of money for 5 years at 3% p.a. is ₹ 54.90. Find the sum.
Let, the sum be 100
Simple interest, SI = PRN
= 100 × $$\frac{3}{100}$$ × 5 = 15
A = P(1 + i)n = 100$$\left(1+\frac{3}{100}\right)^{5}$$ = 100(1.03)5 = 115.93
CI = A – P = 115.93 – 100 = 15.93
Difference between CI & SI = 15.93 – 15= 0.93
If the difference is 0.93 then principal = 100 = 100
If the difference is 54.90 then principal = $$\frac{100 \times 54.9}{0.93}$$ = 5,903

Question 15.
Find the compound interest on ₹ 30,000 at 6% p.a. for 3 years. What is the difference between simple interest and compound interest on the same?
P = 30,000, R = 6% or 0.06, T = 3 years
Simple interest (S.I) = $$\frac{\text { PTR }}{100}$$ = $$\frac{30,000 \times 3 \times 6}{100}$$
= $$\frac{5,40,000}{100}$$ = 5,400
F = P(1 + r)n
= 30,000(1 + 0.06)3 = 30,000 (1.06)3 = 30,000 (1.191) = 35,730
A = F – P
35,730 – 30,000 = 5,730
∴ Difference is 330 because SI. is calculated on same amount but in C.I. they calculated at amount + interest. Hence it differs.

Question 16.
Mrs. Sheela borrowed ₹ 30,000 for 6 years. Calculate compound . interest @ 12% p.a. reckoned quarterly.
Given, A = 30,000, R = 12% p.a., T = 6 years
Now, interest has to be calculated quarterly.
∴ rate of interest = 12/4 = 3%
CI = P$$\left(1+\frac{R}{100}\right)^{\top}$$ – P = 30,000$$\left(1+\frac{3}{100}\right)^{6}$$ – 30,000
= $$\left(30,000 \times\left(\frac{103}{100}\right)^{6}\right)$$ – 30.000 = (30.000 × 1.19) – 30,000
= 35700 – 3000 = 5700
Compound interest = 5700

Question 17.
A company needs ₹ 10,00,000 at the end of 5 years. It would like to set aside an equal amount each year out of its profits. If the present rate of interest is 16%, how much should annual amount be invested?
In this problem we have been given the
Future value of the annuity (f) as ₹ 10,00,000
No. of year n = 5 and r = 16%
We have to find the value of A.
F = $$\frac{A\left[(1+r)^{n}-1\right]}{r}$$
10,00,000 = $$\frac{A\left[(1.16)^{5}-1\right]}{0.16}$$
10,00,000 × 0.16 = A[(1.16)5 – 1] (1.16)5 = A.1(5log 1.16)
= 1,60,000 = A[2,0990 – 1] = A.1(5 × 0.0644)
1.009A = 1,60,000 = A.1(0.3220)
A = $$\frac{1,60,000}{1.099}$$ = 2.0990
A = ₹ 1,45,586.90
The company should set aside a sum of ₹ 1,45,586.90 each year to get ₹ 10,00,000 at the end of 5 years.

Question 18.
A person borrowed ₹ 6,400. After 2 years and three months he paid ₹ 6,136 in cash with a horse and cleared the amount. If the rate of interest was 3 1/2% PA, find the value of the house.
SI = $$\frac{\text { PRN }}{100}$$ = $$\frac{6,400 \times 7 \times 9}{100 \times 2 \times 4}$$ = 504
Amount = 6400 + 504 = 6904
Amount paid = 6134
Value of house = 6904 – 6134 – 770

Problems on Annunity and Bill Discount

Question 19.
Monthly incomes of A and B are in the ration 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves ₹ 500 a month, find the monthly incomes.
Income – Savings = Expeness
Let, Incomes be x
$$\frac{4 x-500}{5 x-500}$$ = $$\frac{7}{9}$$
9(4x – 500) = 7(5x – 500) 36x – 4500 = 35x – 3500
x = 4500 – 3500 = 1000
Income of A = 4x = 4(1000) = ₹ 4000
Income of B = 4x = 5(1000) = ₹ 5000

Question 20.
5 carpenters can earn ₹ 360 in 6 days working 9 hours a day. How much will 8 carpenters earn in 12 days working at 6 hours a day?

 Carpenters Hour Days Wages 5 9 6 360 8 6 12 x

x = 360 × $$\frac{8}{5}$$ × $$\frac{6}{9}$$ × $$\frac{12}{6}$$ = Rs. 768

Question 21.
A man spends 18% of his income for house rent and for other expenses he spends 52% and he saves ₹ 1,500 monthly. Find his monthly income.
Let, monthly income = ₹ 100 Paid house rent = ₹ 18
Other expenses = ₹ 52 Total expense = ₹ (18 + 52) = ₹ 70
When, monthly savings is ₹ 30, income = ₹ 100
When, monthly savings is ₹ 1,500, income = $$\frac{100 \times 1,500}{30}$$ = ₹ 5,000
Hence his monthly income is ₹ 5000.

Question 22.
In a boarding house of 50 members, the total monthly miscellaneous expenses were increased by ₹ 76 when the number of boarders increased by 14, the average monthly miscellaneous expenses were therefore reduced by one rupee per head.
Find the original rate of miscellaneous expenses per head, per month.
Let, total monthly expenditure be x.
average expenditure = $$\frac{x}{50}$$
Now, if the members are increased by 14, the total monthly expenditure increases by 76.
Therefore total monthly expenditure = x + 76
Average monthly expenditure = $$\frac{x+76}{64}$$ = 1
Now as per the given situation, $$\frac{x}{50}$$ – $$\frac{x+76}{64}$$ = 1
64x – 50x – 3800 = 3200
14x = 7000
x = 500
Therefore original average monthly expenditure is 500/50=10

Question 23.
Calculate the present value of an annuity of ₹ 5,000 per annum for 12 years the interest being 4% p.a. compounded annually.
n = 12 years, r = 4% = 4/100 = 0.04, A = ₹ 5,000
P.V = A$$\frac{\left[(1+r)^{n}-1\right]}{r}$$ = 5,000$$\frac{\left[(1+0.04)^{12}-1\right]}{0.04}$$
= 5000$$\frac{\left[(1.04)^{12}-1\right]}{0.04}$$ = ₹ 75129.027

Question 24.
Neeraj’s 2nd Semester (BCU) Scanner A man can purchase 4 kgs more rice for ₹ 250 due to a reduction of 22% is the price. Find the price of rice before and after reduction.
He can save due to a reduction = 22% of ₹ 250 = $$\frac{22}{100}$$ × 250 = ₹ 55
He purchases 4 kgs of rice with ₹ 55
∴ Price per kg = $$\frac{55}{4}$$ = ₹ 13.75
Now, reduced price = 100 – 22 = ₹ 78
When reduced price is ₹ 78, original price = ₹ 100
When reduced price is ₹ 13.75, original price = $$\frac{100 \times 13.75}{78}$$ = ₹ 17.62
Hence, before reduction, the price is. ₹ 17.62.
After reduction, the price is ₹ 13.75.

Question 25.
A man lost 8% by selling an article for ₹ 230. For how much should he have sold it to gain 10%?
₹ 230 = 92%
? for 110%
$$\frac{230}{92}$$ × 110 = 275

Question 26.
Ashok lent two equal sum of money to Rahul and Laxman. While Rahul agreed to pay interest at 5% p.a., Laxman agreed to pay interest at 6%p.a. At the end of 10 years Ashok received ₹ 1,000 more from Laxman towards interest. How much did Ashok lend to Rahul and Laxman each? Interest charged being simple interest.
Principla let n to both Rahul and laxman is the same and let it be denoted by ‘P
∴ Interest due from Laxman is
ILaxman = p r n = P × 0.06 × 10 = 0.6P
Interest from Rahul = IRahul = p r n = P × 0.05 × 10 = 0.5P
It is given that 0.6P – 0.5P = 1000
∴ 0.1P = 1000
P = $$\frac{1000}{0.1}$$ ⇒ P = 10,000
∴ Principal lent to each is ₹ 10,000

Question 27.
A man bought 2 watches for ₹ 400. He sold one at a profit of 10% and the other at a loss of 10% and then he found that each was sold for the same price. Find the cost price of each.
Let, the cost price of 1st watch be x
∴ Cost price of 2nd watch = 400 – x
In the 1st case, he makes a profit of 10%
∴ Selling price of 1st watch = $$\frac{110}{100}$$(x)
In the 2nd case, loss is 10%
∴ Selling price of 2nd watch = $$\frac{90}{100}$$ × (400 – x)
Given, $$\frac{110x}{100}$$ = $$\frac{90}{100}$$ × (400 – x)
⇒ 110x = 90(400 – x) ⇒ 110x = 36,000 – 90x ⇒ 200x = 36,000
∴ x = 180
∴ Cost price of 1st watch is ₹ 180
So, cost price of 2nd watch is ₹ (400 – 180) = ₹ 220

Question 28.
The ratio of prices of 2 vehicles was 8 : 7 Three years later when the price of first had increased by 880 and the second by 10%, the ratio of their prices became 13 : 11. What was the original prices?
Let, the Original price of the 2 vehicles be 8x and 7x. respectively
Three years later
$$\frac{8 x+880}{7 x+\frac{10}{100} \text { of } 7 x}$$ = $$\frac{13}{11}$$
$$\frac{8 x+880}{7 x+0.7 x}$$ = $$\frac{13}{11}$$
⇒ 11(8x + 880) = 13(7x + 0.7x) ⇒ 88x + 9680 = 13×7.7x ⇒ 9680 = 100.1x – 88x
⇒ 12.1x = 9680 ⇒ x = $$\frac{9680}{12.1}$$ ∴ x = 800
Original price of the 2 vehicles are
Ist vehicle = 8x = 8 × 800 = 6400
IInd vehicle and 7x = 7x 800 = 5600

Question 29.
After allowing a discount of 7 1/2% on the marked price of an article, an article is sold for ₹ 555. Find its marked price.
Let, market price x
Discount rate 7 1/2 % = 7.5%
Market price – Discount of M.P. = Price sold
⇒ x – 7.5% = x = 555 ⇒ x – $$\frac{7.5 x}{100}$$ = 555
⇒ $$\frac{92.5 x}{100}$$ = 555 ⇒ 92.5x = 55500 ⇒ x = $$\frac{55,500}{92.5}$$
∴ x = 600
Hence, market price ₹ 600

Question 30.
A machine listed at ₹ 625 was sold at a discount of 15%. Find the discount and the net price.
Discount rate 15%
Total discount = 15% of 625 = 625 × 15/100 = ₹ 93.75
Net price = (625-93.75) = ₹ 531.25

Question 31.
A bill for ₹ 12,750 drawn on May 27th for 4 months was discounted on July 19th at 4% p.a Find:
i) Banker’s discount
ii) True Discount
iii) Bankers gain
iv) The amount received by the holder of the bill.
A = 12750 The date on which the bill is drawn = may 27
R = 4% The date on which the bill is due Sep 30
N = ? The date on which the bill is discounted = July 19
Un Expored period July 19 to Sep.30
July + Aug + Sep
12 + 31 + 30 = 73 days
BD = $$\frac{12750 \times \frac{1}{5} \times 4}{100}$$ = ₹ 102
TD = $$\frac{\text { ANR }}{100+N R}$$ = $$\frac{12750 \times \frac{1}{5} \times 4}{100+\frac{4}{5}}$$ = 101.19
BG = BD – TD 102 – 10 – 101.19 = 0.81
Amount received by the holder of the bill = 12750 – 102 = Rs 12548

Question 32.
The Banker’s gain on a bill due 6 months is ₹ 40 and the rate of interest being 20% p.a. Find the face value of the bill.
Given, BG = ₹ 20
T = 6 month = 1/2 years
R = 20% = 0.20
The equation BG = TD × T × R
20 = 0.10 × T.D.
T.D. = $$\frac{20}{0.10}$$ = ₹ 200
Here, BG = BD – TD
BD = TD + BG = 200 + 20 = ₹ 220
Now, Banker’s discount BD = F × T × R
⇒ 220 = F × 1/2 × 0.20
⇒ 220 = F × 0.10
⇒ F = $$\frac{220}{0.10}$$
∴ F = 2200 So, Face value of the bill ₹ 2200

Question 33.
A man sold 2 ratios at ₹ 924 each. One he gains 20% and on another he loses 20%. How much does he gains or lose on the whole transaction?
Selling price of 1st Ratio = ₹ 924
Gain = 20%
Let the cost price by x
∴ x + $$\frac{20}{100}$$x = 924 $$\frac{6x}{5}$$ = 770
x = 770
Gain = 924 – 770 = ₹ 154
Selling price of 2nd radio = ₹ 924
Loss = 20%
Let the cost be y
(ii) True discount (TD)
TD = PTR = 19,952 × 0.67 × 0.06 = 802
(iii) Banker Discount (BD)
BD = F + R = 20,750 × 0.67 × 0.06 = 834
(iv) Bank’ers gain (BG)
BG = BD – TD = 834 – 802 = 32
Working note:
Present value = ?
Given,
Time (t) = $$\frac{8}{12}$$ = 0.6666 = 0.67
Interest of rate (1) = 6% = $$\frac{6}{100}$$ = 0.06
Face Value (F) = 20,750
a) y-20/100 = 924
$$\frac{4 y}{5}$$ = 924
y = ₹ 1,155
Loss = 1,155 – .924 = ₹ 231
Since loss is greater than gain, the whole transaction resulted in a loss of ₹ 231- ₹ 154 = ₹ 77

Question 34.
What is the face value of the bill discounted at 5% p.a. 73 days earlier than the date of maturity, the banker’s gain being ₹ 10 only?
Let, Face, value, F
Rate of interest R = 5%
Time period, T = 73 days
Banker gain = ₹ 10
Banker gain = True discount × T × R
⇒ 10 = TD × $$\frac{73}{365} \times \frac{5}{100}$$ ⇒ 10 = $$\frac{365 \times \text { TD }}{365 \times 100}$$ ⇒ TD = 1,000
Again,
Banker gain = Banker discount – TD
10 = BD – 1,000 ⇒ BD = 1000 – 10 = 990
Face value of the bill:
BD = F × T × R
990 = F × $$\frac{73}{365} \times \frac{5}{100}$$ ⇒ 990 = $$\frac{F}{100}$$ ⇒ F = 990 × 100
∴ F = 99,000
Hence, Face value of the bill = ₹ 99,000

Question 35.
A bill for ₹ 14,600 drawn at 3 months was discounted on November 11th for ₹ 14,544. If the role of simple interest is 4% p.a., on what date was the bill drawn.
Given, Face value of the bill, A = 14,600
Amount paid by the banker = 14,544
Banker’s discount = 56, R = 4%
B.D = $$\frac{\text { ANR }}{100}$$
56 = $$\frac{14,600 \times N \times 4}{100}$$
⇒ 584N = 56 ⇒ N = $$\frac{56}{584}$$ × 365 days ∴ N = 35 days
∴ The date on which nominally due to 16th December (Nov. 11th + 35 days)
To find the date on which the bill is drawn, subtract 3 months from 9th Dec.
∴ The date is 9th September.

Question 36.
A bill for ₹ 1,450 drawn at 3 months was discounted for ₹ 1,444 at 4% p.a. on 9th November 1985. Find the date on which the bill is drawn.
Given,
Face value of the bill, A = ₹ 1,450
Amount paid by the banker = ₹ 1,444
Banker’s discount = ₹ 6; R = 4%
∴ BD = $$\frac{\text { ANR }}{100}$$ ⇒ 6 = $$\frac{1,450 \times N \times 4}{100}$$ ⇒ 58N = 6 ⇒ N = $$\frac{6}{58}$$ × 365 days
∴ N = 37.75 = 38 days
∴ The date on which the bill falls due is = 9th Nov. + 38 days = 17th Dec.
Hence, the bill is nominally due on 17th Dec. (including 7 grace days).
To find the date on which the bill is drawn, subtract 3 months from 10th December.
∴ The date is 10th September.

Question 37.
If the interest is 6% compounded annually, then how many annual payments of ₹ 56 each are needed to accumulate ₹ 2,500?
Given, a = 56, A = 2,500 ; i = 0.06
We know that, A = $$\frac{a}{i}$$[(1 + i)”-1] = 2,500 = $$\frac{56}{0.06}$$ [1 + 0.06)” – 1]
⇒ 2,500 = 933.33 [(1.06)n – 1] ⇒ (1.06)n – 1 = 2.678
⇒ (1.06)” = 3.678
Take logarithm in both sides N log 1.06 = log 3.678 ⇒ n = $$\frac{\log 3.678}{\log 1.06}$$
∴ n = 22.35
∴ After 22 payments, the sum will be nearer to ₹ 2,500

Problems on Ratio and Proportion

Question 38.
If 12 men or 15 women can finish a work in 66 days, how long will 24 men and 3 women take to finish the work.
Given 12 men = 15 women
1 man = 1.25 women
∴ 24 men and 3 women = 33 women
Let, 33 women can do work in X. days.
here, number of women increase, days will decreases.
33 : 66 = 15 : x
⇒ $$\frac{33}{66}$$ = $$\frac{15}{x}$$
⇒ 33x = 990
⇒ x = $$\frac{990}{33}$$ ∴ x = 30 days

Question 39.
If 15 men working 12 hours per day perform a job in 16 days, how long will it take 21 men working 10 hours daily to do the same task?
This is a case of compound proportions because, there are three quantities in relationship with each other, number of men, number of hour per day and number of days worked.
Let the number of days required for 21 men working 10 hours per day = x days.
Step 1: Express the odd term and unknown quantity as the third and fourth proportional.
∴ 16 days : x days
Step 2: Take the known quantities and express them as ratios, arranging the terms in the order of ratios in stepl. Keep the relationship, i.e., direct or inverse, in mind while writing ratios.
(i) Number of men is inversely proportional to number of days, in doing a job.
∴ 21 : 15 :: 16 : x
(ii) Number of hours per day and the number of days to do a job are inversely related
∴ 10 : 12 :: 16 : x
(iii) $$\left\{\begin{array}{l} 21: 15 \\ 10: 12 \end{array}\right\}$$ :: 16 : x
Step 3: Compound the left hand side ratio
⇒ (21 × 10) : (15 × (12) :: 16 : x ⇒ 210 : 180 :: 16 : x
∴ x = $$\frac{180 \times 16}{210}$$ = 13.71 days

Question 40.
If 10 men can earn ₹ 10,500 in 7 days, in how many days will 15 men earn ₹ 22,500?
Let the numbers of days required for 15 men be x.
Then, The third proportional term = 7 days
Fourth term = x days
Therefore the ratio = 7 : x
(i) The known ratio of like items are
(a) Number of men (inverse proportional)
= 15 : 10
(b) Amount earn (direct proportional)
= 10500 : 22500
Then, 15 : 10 :: 7 : x (1)
10500 : 22500 :: 7 : x (2)
From (1) and (2) we get
(15 × 10500) : (10 × 22500) :: 7 : x
⇒ 157500 : 225000 :: 7 : x ⇒ 157500x = 225000 × 7
∴ x = $$\frac{225000 \times 7}{157500}$$ = 10 days

Question 41.
The ratio of the students in Arts, Science and Commerce faculties is 5 : 4 : 3. If the number of students in Science faculty is 236,
find the number of students in Arts and Commerce faculties.
Let x be the number of students in all faculties.
The continued ratio of the students of Arts, Science and Commerce faculty = 5 : 4 : 3
Sum of the terms = 5 + 4 + 3 = 12
Given, Number of students in Science = $$\frac{x}{12}$$ × 4 = 236
i.e., x = $$\frac{236 \times 12}{4}$$ ∴ x = 708
Thus, number of students in Arts = $$\frac{x}{12}$$ × 5 = $$\frac{708}{12}$$ × 5 = 295
Number of students is Commerce = $$\frac{x}{12}$$ × 3 = $$\frac{708}{12}$$ × 3 = 177
Hence, the number of students is Arts and Commerce faculties are 295 and 177.

Question 42.
18 note books cost as much as 5 dot pens and 12 dot pens cost as much as. 4 pencils. If the cost of 2 pencils is ₹ 25. Find the cost of a note book.
Let, x be the cost of a note book.
i.e., cost of 1 note book = ₹ x
Given, Cost of 18 note books = Cost of 5 dot pens
Cost of 2 pencils = ₹ 25
Cost of 12 dot pens = Cost of 4 pencils
So, it is a compound proportion.
We have,
x × 18 × 2 × 12 = 1 × 5 × 25 × 4
⇒ x = $$\frac{1 \times 5 \times 25 \times 4}{18 \times 2 \times 6}$$
∴ x = 1.15
∴ Cost of a note book is ₹ 1.15.

Question 43.
If 12 pumps working 7 hours a day can lift 2800 tonnes of water in 20 days, in how many days can 20 pumps working 9 hours a day lift 3000 tonnes?
It is the problem of direct ratio and inverse ratio.
Let the no. of days required be x
12 pumps : 20. pumps :: x : 20……….(1)
3000 tonnes : 2800 tonnes :: x : 20………….(2)
7 hours : 9 hours :: x : 20………….(3)
From (1), (2) and (3) we get
x = $$\frac{12 \times 3000 \times 7 \times 20}{20 \times 2800 \times 9}$$ = 10 days
No. of days required = 10

Question 44.
A purse contains some coins consisting of 50 paise, 25 paise and 10 paise pieces.
If the coins be in the ratio 3 : 4 : 5 and their total value be 144. Find the number of coins of each kind.
∴ Ratio of value = 3 × $$\frac{1}{2}$$ : 4 × $$\frac{1}{4}$$ : 5 : $$\frac{1}{10}$$ = 3 : 2 : 1
Value of 50 paise coins = $$\frac{3}{6}$$ × 144 = ₹ 72
Value of 25 paise coins = $$\frac{2}{6}$$ × 144 = ₹ 48
Value of 10 paise coins = $$\frac{1}{6}$$ × 144 = ₹ 24