Question 1

Jagmohan, Rooplal and Pandeyji rented a video cassette for one week at a rent of Rs. 350. If they use it for 6 hours, 10 hours and 12 hours respectively. The rent to be paid by Pandeji is?

Accepted Answer

Ratio of rent = 6 : 10 : 12 = 3 : 5 : 6 ∴ Pandeyji has to pay = Rs. 350 x (6/14) = Rs. 150

Question 2

A and B invest Rs. 3000 and Rs. 4000 in a business. A receives Rs. 10 per months out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investment. In a year A totally receives Rs. 390. Wh…

Accepted Answer

Total profit - Remuneration = Balance profit This balance profit is divided in proportion to their investment ∴ (Balance Profit of A) / (Balance Profit of B) = (Investment of A) / (investment of B) ⇒ (390 - 10 x 12) / balance of Profit of B = 3000/4000 = 3/4 (Since remuneration of A is Rs. 10 per month) ⇒ Balance profit of B = (4 x 270)/3 = Rs. 360 Since B does not get any remuneration, hence B receives Rs. 360 at the end of the year.

Question 3

A starts a business with ₹ 4000. B joins him after 3 months with ₹ 8000. C puts a sum of ₹ 20000 in the business for 2 months only. At the end of year, the business gives a profit of ₹ 16800. How should the profit be divided amongst them?

Accepted Answer

A's share : B's share : C's share = Ratio of product of investment and time period of investment = 4000 x 12 : 8000 x (12 - 3) : 20000 x 2 = 4 x 12 : 8 x 9 : 20 x 2 = 6 : 9 : 5 Let, A's share = 6N B's share = 9N C's share = 5N According to the question, 6N + 9N + 5N = 16800 ⇒ 20N = 16800 ∴ N = 16800/20 = 840 ∴ A's share = 6N = 6 x 840 = ₹ 5040 B's share = 9N = 9 x 840 = ₹ 7560 C's share = 5N = 5 x 840 = ₹ 4200

Question 4

P, Q and R start a business jointly. Twice the capital of P is equal to thrice the capital of Q and the capital of Q is four times the capital of R. Find the share of Q in an annual profit of ₹ 148500.

Accepted Answer

Let R's capital = 1 Then, Q's capital = 4 2 (P's capital) = 3 (Q's capital) = 3 x 4 = 12 ∴ P's capital = 12/2 = 6 ∴ P's share : Q's share : R's share = 6 : 4 : 1 Thus, Q's share profit = { 4/(6 + 4 + 1)} x 148500 = (4/11) x 148500 = 4 x 13500 = ₹ 54000

Question 5

M, N and P invest ₹ 50000 for a business. M invests ₹ 4000 more than N and N invest ₹ 5000 more than P. Out of the total profit of ₹ 70000, what is the share received by M?

Accepted Answer

Let investment of P = ₹ K Then, investment of N of = ₹ (K + 5000) and investment of M = (K + 5000) + 4000 = ₹ (K + 9000) According to the question. K + (K + 5000) + (K + 9000) = 50000 ⇒ 3K + 14000 = 50000 ⇒ 3K = 50000 - 14000 = 36000 ∴ K = 36000/3 = 12000 Clearly, investment of P = ₹ 12000 Investment of N = (K + 5000) = 12000 + 5000 = ₹ 17000 Investment of M = (K + 9000) = 12000 + 9000 = ₹ 21000 M's share : N's share : P's share = 21000 : 17000 : 12000 = 21 : 17 : 12 Hence, M's share = [21/(21 + 17 + 12 )] x 70000 = (21/50) x 70000 = ₹ 29400

Question 6

P, Q and R hire a meadow for ₹ 2920. P puts 10 cows for 20 days, Q puts 30 cows for 8 days and R puts 16 cows for 9 days. Find the rent paid by R.

Accepted Answer

Ratio of rents to be paid by P, Q and R Ratio of monthly equivalent = (10 x 20) : (30 x 8) : (16 x 9) = 200 : 240 : 144 = 25 : 30 : 18 Hence R's share = [18/(25 + 30 + 18)] x 2920 = (18/73) x 2920 = 18 x 40 = ₹ 720

Question 7

A, B and C enter into a partnership. A invests some amount at the beginning, B invests double the amount of A after 6 months and C invests thrice the amount of A after 8 months. If the annual profit be ₹ 54000, find the C's share.

Accepted Answer

Let investment of A = N, Investment of B = 2N, Investment of C = 3N, ∴ A's share : B's share : C's share = (N x 12) : (2N x 6) : (3N x 4) = 12N : 12N : 12N = 1 : 1 : 1 ∴ C's share = [1/(1 + 1 + 1)] x 54000 = (1/3) x 54000 = ₹ 18000

Question 8

A. B and C together start a business. B invests of 1/6 of the total capital while investments of A and C are equal. If the annual profit on this investment is ₹ 33600, find the difference between the profits of B and C.

Accepted Answer

Given, Investment of B = 1/6 of total capital ∴ Investments of A and C each = 1/2(1 - 1/6) of total capital = (1/2) x (5/6) of total capital = (5/12) of total capital Now. A's share : B's share : C's share = (5/12) : (1/6) : (5/12) = 5 : 2 : 5 Let A's share = 5N B's share = 2N C's share = 5N According to the question. 5N + 2N + 5N = 33600 ∴ 12N = 33600 ∴ N = 33600/12 = 2800 ∴ Difference in the profits of B and C = 5N - 2N = 3N = 3 x 2800 = ∴ 8400

Question 9

A and B invest in a business in the ratio of 3 : 2. If 5% of the total profit goes to a charity and A's share is ₹ 4275, then what will be the total profit?

Accepted Answer

Let total profit = N Paid to charity = 5% of N = (5 x N)/100 = N/20 ∴ Balance profit = N - N/20 = 19N/20 ∴ A's share = (19N/20) x (3/5) = 57N/100 According to the question. 57N/100 = 4275 ∴ N = (4275 x 100)/57 = 7500 Hence. total profit = ₹ 7500

Question 10

A and B together start a business by investing in the ratio of 4 : 3. If 9% of the total profit goes to charity and A's share is ₹ 1196, find the total profit.

Accepted Answer

Let total profit = N Paid to charity = 9% of N = 9N/100 ∴ Balance profit = N - (9N/100) = 91N/100 ∴ A's share = [4/(4 + 3)] x (91N/100) = (4/7) x (91N/100) According to the question, (4/7) x (91N/100) = 1196 ∴ N = (1196 x 7 x 100)/(4 x 91) = ₹ 2300 Hence, total profit = ₹ 2300

Question 11

A, B and C do certain investments for time periods in the ratio of 2 : 1 : 8. At the and of the business term, they received the profits in the ratio of 3 : 4 : 2. Find the ratio of investments of A, B and C.

Accepted Answer

Let required ratio of investments be I1 : I2 : I3. Ratio of investments = Ratio of profits 2I1 : I2 : 8I3 = 3 : 4 : 2 Taking first two terms of the ratio (2I1) / I2 = 3/4 ⇒ I1 / I2 = 3/8 = 6/16 ⇒ I1 : I2 = 6 : 16 Taking last two terms of the ratio , I2 / (8I3) = 4/2 ⇒ I2/I3 = 16/1 ⇒ I2 : I3 = 16 : 1 ∴ I1 : I2 : I3 = 6 : 16 : 1

Question 12

A and B started a business by investing ₹ 20000 and ₹ 25000, respectively. After 4 months B left and C joined by investing ₹ 15000. At the end of the year, there was a profit of ₹ 23000 What is C's share?

Accepted Answer

A's share : B's share : C's share = (20000 x 12) : (25000 x 4) : (15000 x 8) = 240000 : 100000 : 120000 = 24 : 10 : 12 = 12 : 5 : 6 Let A's share = 12N B's share = 5N C's share = 6N According to the question. 12N + 5N + 6N = 23000 ⇒ 23N = 23000 ∴ N = 23000/23 = 1000 ∴ C's share = 6N = 6 x 1000 = ₹ 6000

Question 13

A and B started a business by investing ₹ 35000 and ₹ 20000, respectively. After 5 months B left the business and C joined the business with a sum of ₹ 15000. The profit earned at the end of year is ₹ 84125. What is the share of B in profit?

Accepted Answer

Ratio of equivalent capitals of A, B and C = (35000 x 12) : (20000 x 5) : (15000 x 7) = 35 x 12 : 20 x 5 : 15 x 7 = 84 : 20 : 21 Let A's share = 84N B's share = 20N C's share = 21N According to the question, 84N + 20N + 21N = 84125 ⇒ 125N = 84125 ⇒ N = 84125/125 = 673 ∴ B's share = 20N = (20 x 673) = ₹ 13460

Question 14

P and Q make a partnership, P invests ₹ 8000 for 8 months and Q remains in the business for 4 months. Out of the total profit, Q claims 2 / 7 of the profit. How much money was contributed by Y?

Accepted Answer

Q gets 2/7 of the profit. ∴ P gets(1 - 2/7) = 5/7 of the profit ∴ P : Q = 5/7 : 2/7 = 5 : 2 Let the contribution of Q be a. Then, 8000 x 8 : a x 4 = 5 : 2 ⇒ 64000/4a = 5/2 ⇒ 20a = 128000 ∴ a = 128000/20 = ₹ 6400

Question 15

A and B invest ₹ 3000 and ₹ 4000, respectively in a business. A receives ₹ 10 per month out of the profit as a remuneration for running the business and the rest of the profit is divided in proportion to the investments. If in a year A totally recei…

Accepted Answer

Let the annual profit be ₹ N Then, ₹ (N - 120) will be distributed between A and B as their shares of profit. Ratio of profits = Ratio of investments So, A : B = 3000 : 4000 = 3 : 4 ∴ A's share = 120 + (N - 120) x 3/7 ⇒ 120 + (N - 120) x 3/7 = 390 ⇒ (N - 120) x 3/7 = 390 - 120 = 270 ⇒ N - 120 = (270 x 7)/3 = 630 ∵ B's share = 4/7 x (N - 120) = (4/7) x 630 = ₹ 360

Question 16

Amit and Brijesh started a business with initial investments in the ratio of 12 : 11 and their annual profits were in the ratio of 4 : 1. If Amit invested the money for 11 months, then for what time Brijesh invested the money?

Accepted Answer

Let investment of Amit = 12k and investment of Brijesh = 11k Let Brijesh invested the money for N months. Then, Amit's investment : Brijesh's investment = (12k x 11) : (11k x N) = 132k : 11kN = 12 : N ∴ 12/N = 4/1 [ ∵ ratio of profit is 4 : 1] ⇒ 4N = 12 ∴ N = 12/4 = 3 months Clearly, Brijesh invested money for 3 months.

Question 17

Amitabh, Brijesh and Kamlesh enter a partnership with shares in the ratio of 7/2 : 4/3 : 6/5. After 4 months, Amitabh increases his share by 50% If the total profit at the end of the year be ₹ 21600, what will be the share of Brijesh in the profit?

Accepted Answer

Given. ratio = 7/2 : 4/3 : 6/5 = (7/2) x 30 : (4/3) x 30 : (6/5) x 30 = 105 : 40 : 36 Let investment of Amitabh = 105k Investment of Kamlesh = 36k Ratio of their investments = [105k x 4 + 150% x8 of 105k] : (40k x 12) : (36k x 12) = (420k + (150/100) x 105k x 8) : (480k) : (432k) = (1680k) : (480k) : (432k) = 35 : 10 : 9 ∴ Brijesh's share = (21600 x 10) / (35 + 10 + 9) = (21600 x 10) / 54 = ₹ 4000

Question 18

A and B started a joint business. A's investment was thrice the investment of B and the period of his investment was twice the period of investment of B. If B got ₹ 6000 as profit, then what will be the 20% of total profit?

Accepted Answer

Let investment of B be a for b months. Then, A's investment = 3a for 2b months ∴ A : B = (3a x 2b) : (a x b) = 6ab : ab = 6 : 1 Let the total profit = m. Then. m x 1/7 = 6000 ∴ m = 6000 x 7 = ₹ 42000 ∴ 20% of 42000 = ₹ 8400

Question 19

A and B entered a partnership investing ₹ 16000 and ₹ 12000, respectively. After 3 months A takes out ₹ 5000, while B puts in ₹ 5000 more. After 3 months more. C joins the business with a capital of ₹ 21000. After a year, they earned a profit of ₹ 1…

Accepted Answer

A's share : B's share : C's share = [16000 x 3 + (16000 - 5000) x 9] : [12000 x 3 + (12000 + 5000) x 9] : (21000 x 6) = (16 x 3 + 11 x 9) : (12 x 3 + 17 x 9) : (21 x 6) = 147 : 189 : 126 = 7 : 9 : 6 Hence, B's share exceeds C's share by = {13200/(7 + 9 + 6)} x (9 - 6) = (13200 x 3)/22 = ₹ 1800

Question 20

Two partners invest ₹ 125000 and ₹ 85000, respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets ₹ 600 more than the ot…

Accepted Answer

The difference counts only due to 40% of the profit which was distributed according to their investments. Let total profit = R. 40% of R is distributed in the ratio, 125000 : 85000 = 25 : 17 Share of 1st partner = 40% of R x25/(25 + 17) = 40% of 25R/42 = (40/100) x (25R/42) = 5R/21 Share of 2nd partner = 40% of 17R/42 = (40/100) x (17R/42) = 17R/105 Now according to the question 5R/21 - 17R/105 = 600 ⇒ R(25 - 17)/105 = 600 ⇒ R = (600 x 105)/8 = ₹ 7875

Partnership Questions