chart given below shows distribution (in degree) of capital amount of all the five persons P, Q, R, S and T respectively in business A and line graph given below shows capital amount of all the five persons P, Q, R, S and T respectively in business B.

Sum of capital amount invested by all the five persons together in business A = Rs.1.2 lakhs

Note: All the data given in the line graph are in thousand.

* It is not necessary that all the five persons started the business A and B. Any combination of persons can start the business and a person may or may not take part in the business. Pie chart and line graph shows only the first-time investment of a person when he starts the business or enters into a business that is already started and he can change his investment further in the business. It is also not necessary that the time period for which persons invested their capital in any business is same.

1) Persons Q and T started business A and after 2 years T, left and at the same time P and R joins the business. After one more year, person S also joins the business, then out of total profit of Rs.74700 at the end of 5 years from the start of the business, what is the difference between the profit share of P and R together and profit share of T and S together?

a) Rs.2790

b) Rs.2900

c) Rs.2970

d) Rs.2700

e) None of these

2) Person R started business A while at the same time person Q stared business B. After 5 years, person Q joins business A while person R joins business B. If total profit from business A at the end of 15 years is Rs.41400 and profit from business B at the end of 10 years is Rs.66000, then what is the ratio of profit share of Q to that of R from both the businesses together?

a) 62: 35

b) 104: 75

c) 20: 9

d) 224: 125

e) None of these

3) If person P stared business A and person T started business B simultaneously. After 3 years, person Q joins business A and at the same time person S joins business B. If profit share of person P from business A at the end of 6 years is Rs.8100 and profit share of person T from business B at the end of 5 years is Rs.4050, then what is the difference between profit amount from business A after 6 years and that from business B after 5 years?

a) Rs.4240

b) Rs.3620

c) Rs.4320

d) Rs.4860

e) None of these

4) Persons R and S started a business A with their mentioned initial capital and after 4 years, R withdraws Rs.13750 from his capital and S withdraws Rs.6250 from his capital. At the same time person T joins that business with R and S. Total profit received from the business after 8 years from the start is Rs.67200, then what will be the change in the profit amount of T if both R and S didn’t change their capital when he joined the business?

a) Rs.3584

b) Rs.2672

c) Rs.3624

d) Rs.2892

e) None of these

5) Person P and R stared a business B where P is sleeping partner and R is active partner. After ‘n’ years, person T also joins business with P and R as an active partner. Since, R and T are active partners so, R will get Rs.5400 and T will get Rs.27000 as their salary. Now, ratio of profit share (including salary) of P, R and T after 15 years will become 7: 7: 8 respectively and total profit from the business is Rs.118800, then what is the value of ‘n’?

a) 8

b) 6

c) 9

d) 4

e) None of these

Answers :

Directions (1-5):

Capital of P in business A = 120000 * (72/360) = Rs.24000

Capital of Q in business A = 120000 * (48/360) = Rs.16000

Capital of R in business A = 120000 * (60/360) = Rs.20000

Capital of S in business A = 120000 * (75/360) = Rs.25000

Capital of T in business A = 120000 * (105/360) = Rs.35000

Capital of P in business B = Rs.28000

Capital of Q in business B = Rs.32000

Capital of R in business B = Rs.24000

Capital of S in business B = Rs.30000

Capital of T in business B = Rs.20000

1) Answer: D

Weightage of profit share of P = 24000 * 3 = 72000

Weightage of profit share of Q = 16000 * 5 = 80000

Weightage of profit share of R = 20000 * 3 = 60000

Weightage of profit share of S = 25000 * 2 = 50000

Weightage of profit share of T = 35000 * 2 = 70000

Ratio of their profit share = 72: 80: 60: 50: 70 = 36: 40: 30: 25: 35

Profit share of P and R together = 74700 * [(36 + 30)/(36 + 40 + 30 + 25 + 35)] = Rs.29700

Profit share of T and S together = 74700 * [(35 + 25)/(36 + 40 + 30 + 25 + 35)] = Rs.27000

Required difference = 29700 – 27000 = Rs.2700

2) Answer: B

Business A:

Weightage of profit share of Q = 16000 * 10 = 160000

Weightage of profit share of R = 20000 * 15 = 300000

Ratio of profit = 16: 30 = 8: 15

Business B:

Weightage of profit share of Q = 32000 * 10 = 320000

Weightage of profit share of R = 24000 * 5 = 120000

Ratio of profit = 32: 12 = 8: 3

Profit share of Q from both the businesses together = [41400 * (8/23)] + [66000 * (8/11)] = 14400 + 48000 = Rs.62400

Profit share of R from both the businesses together = (41400 + 66000) – 62400 = Rs.45000

Required ratio = 62400: 45000 = 104: 75

3) Answer: C

Business A:

Weightage of profit share of P = 24000 * 6 = 144000

Weightage of profit share of Q = 16000 * 3 = 48000

Ratio of profit = 144: 48 = 3: 1

Total profit from business A after 6 years = 8100 * (4/3) = Rs.10800

Business B:

Weightage of profit share of T = 20000 * 5 = 100000

Weightage of profit share of S = 30000 * 2 = 60000

Ratio of profit = 10: 6 = 5: 3

Total profit from business B after 5 years = 4050 * (8/5) = Rs.6480

Required difference = 10800: 6480 = Rs.4320

4) Answer: A

Ratio of profit share when R and S didn’t change their capital = [20000 * 8]: [25000 * 8]: [35000 * 4] = 16: 20: 14 = 8: 10: 7

Profit share of T when R and S didn’t change their capital = 67200 * (7/25) = Rs.18816

Ratio of profit share when R and S change their capital = [20000 * 4 + 6250 * 4]: [25000 * 4 + 18750 * 4]: [35000 * 4] = 105: 175: 140 = 3: 5: 4

Profit share of T when R and S change their capital = 67200 * (4/12) = Rs.22400

Required change = 22400 – 18816 = Rs.3584

5) Answer: B

Profit share of P = 118800 * (7/22) = Rs.37800

Profit share of Q = 118800 * (7/22) = Rs.37800

Profit share of R = 118800 * (8/22) = Rs.43200

Actual profit of P without salary = Rs.37800 (Sleeping partner)

Actual profit of Q without salary = 37800 – 5400 = Rs.32400

Actual profit of R without salary = 43200 – 27000 = Rs.16200

Actual ratio of their profit share = [28000 * 15]: [24000 * 15]: [20000 * (15 – n)] = 378: 324: 162 = 7: 6: 3

[24000 * 15]: [20000 * (15 – n)] = 6: 3 = 2: 1

360000 = 600000 – 40000n

40000n = 240000

n = 6