Question 1

Four milkmen rented a pasture. A grazed 18 cows for 4 months, B grazed 25 cows for 2 months, C grazed 28 cows for 5 months and D grazed 21 cows for 3 months. If A's share of rent is ₹ 720, what will be the total rent of the pasture?

Accepted Answer

Ratio of rents of A, B, C and D = (18 x 4) : (25 x 2) : (28 x 5) : (21 x 3) = 72 : 50 : 140 : 63 Let the total rent be N. Then, A's share = [72N / (72 + 50 + 140 + 63)] = 72N/325 According to the question. 72N/325 = 720 ∴ N = (720 x 325)/72 = 3250 ∴ Total Rent = ͭ 3250

Question 2

A, B and C invested their capitals in the ratio of 5 : 6 : 8. At the end of the business, they received the profits in the ratio of 5 : 3 : 1. Find the ratio of time for which they contributed their capitals. `

Accepted Answer

Here, p1 : p2 : p3 = 5 : 3 : 1 and x1 : x2 : x3 = 5 : 6 : 8 According to the formula, Required ratio = p1/x1 : p2/x2 : p3/x3 = 5/5 : 3/6 : 1/8 = 1 : 1/2 : 1/8 = 8 : 8/2 : 8/8 = 8 : 4 : 1

Question 3

Sonu invested 10% more than the investment of Mona and Mona invested 10% less than the investment of Raghu. If the total investment of all the three persons is ₹ 5780, find the investment of Raghu.

Accepted Answer

Let share of Raghu be 100. Then share of Mona = 90 and share of Sonu = 99 Sonu : Mona : Raghu = 99 : 90 : 100 ∴ Investment of Raghu = [100/(99 + 90 + 100)] x 5780 = (100/289) x 5780 = ₹ 2000

Question 4

A, B and C entered into partnershp in a business. A got 3/5 of the profit. B and C distributed the remaining profit equally. if C got ₹ 400 less than A, the total profit was

Accepted Answer

Let the total profit be ₹ N, Then, A's share in profit = ₹ 3N/5 Remaining profit = N - 3N/5 = (5N - 3N) / 5 = 2N/5 ∴ B's share in profit = ₹ N/5 C's share in profit = ₹ N/5 According to the question, (3N/5 - N/5) = 400 2N/5 = 400; N = (400 x 5)/2 = ₹ 1000

Question 5

A began a business with ₹ 2250 and was joined afterwards by B with ₹ 2700. If the profits at the end of the year were divided in the ratio of 2 : 1, after how much time B joined the business?

Accepted Answer

Let B remained in the business for N months. Then, A : B = (2250 x 12) : (2700 x N) ⇒ 2 : 1 = (27000 : 2700N) = (10 : N) ∴ 10/N = 2/1 [ ∵ Ratio of profit is 2 : 1] ⇒ 2N = 10 ∴ N = 10/2 = 5 Clearly, B joined after (12 - 5) = 7 months.

Question 6

A, B and C invested capitals in the ratio of 4 : 6 : 9. At the end of the business term, they received the profit in the ratio of 2 : 3 : 5. Find the ratio of their time for which they contributed their capitals.

Accepted Answer

Here, P1 : P2 : P3 = 2 : 3 : 5 [profit's ratio] and x1 : x2 : x3 = 4 : 6 : 9 [investment's ratio] According to the rule, Required ratio = P1/x1 : P2/x2 : P3/x3 = 2/4 : 3/6 : 5/9 = 1/2 : 1/2 : 5/9 = 9 : 9 : 10

Question 7

Aarti, Vinita and Kamla became partners in a business by investing money in the ratio of 5 : 7 : 6. Next year, they increased their investments by 26%, 20% and 15%, respectively. In what ratio should profit earned during 2nd year be distributed?

Accepted Answer

Let investment of Aarti during first year = 5a Investment of Vinita during first year = 7a Investment of kamla during first year = 6a Then, their investments during second year are ⇒ (126/100) x 5a : (120/100) x 7a : (115/100) x 6a = 630 : 840 : 690 = 21 : 28 : 23

Question 8

Anil is an active and Vimal is a sleeping partner in a business. Anil invests ₹ 12000 and Vimal invests ₹ 20000. Anil receives 10% profit for managing, the rest being divided in proportion to their capitals. Out of the total profit of ₹ 9000, the mo…

Accepted Answer

For management, money received by Anil = 10% of 9000 = ₹ 900 Balance = ₹ (9000 - 900) = ₹ 8100 Now, ratio of investments =12000 : 20000 = 3 : 5 ∴ Anil's share = ₹ 8100 x 3/(3 + 5) = ₹ 8100 x 3/8 = ₹ 3037.50 ∴ Amount received by Anil = ₹ 900 + 3037.50 = ₹ 3937.50

Question 9

Aayush and Babloo are partners in a business. Aayush contributes 1/4 of the capital for 15 months and Babloo received 2/3 of the profit. How long Babloo's money was used?

Accepted Answer

Let the total capital be ₹ R and Babloo's money is used for N months. Capital of Aayush = R/4 ∴ Capital of Babloo = (R - R/4) = 3R/4 Ratio of investments of Aayush and Babloo = (R/4) x 15 : (3R/4 x b) = 15/4 : 3N/4 = 5 : N Ratio of profits of Aayush and Babloo = (1/3) : (2/3) = 1 : 2 ∴ 5/N = 1/2 ∴ N = 10 months Hence, Babloo's money was used for 10 months.

Question 10

A and B started a business with ₹ 20000 and ₹ 35000 respectively. They agreed to share the profit in the ratio of their capital. C joins the partnership with the condition that A, B and C will share profit equally and pays ₹ 220000 as premium for th…

Accepted Answer

Ratio of total capital of A and B = 20000 x 12 : 35000 x 12 = 240000 : 420000 Now, C gives ₹ 220000 to both to make the capital equal. ∴ A's capital : B's capital = 240000 + 200000 : 420000 + 200000 = 440000 : 440000 If A takes ₹ 200000 and B takes ₹ 20000 from C, then both have the equal capital ∴ Required ratio of divided amount = 200000 : 20000 = 20 : 2 = 10 : 1 Hence. A and B should divide the amount in the ratio of 10 : 1.

Question 11

P and Q entered a partnership for 3 yr. At the start of the business, they invested ₹ 13000 and ₹ 25000, respectively. At the end of 3 yr their total profit was ₹ 76000. What will be share of Q out of this profit?

Accepted Answer

P's share : Q's share = Ratio of their investments = 13000 : 25000 = 13 : 25 Now, let P's share = 13N Q's share = 25N According to the question, 13N + 25N = 76000 ⇒ N = 76000/38 = 2000 ∴ Q's share = 25N = 25 x 2000 = ₹ 50000

Question 12

Rajan and Sajan started a business initially with ₹ 14200 and ₹ 15600, respectively. If total profits at the end of year is ₹ 74500, what is the Rajan's share in the profit?

Accepted Answer

Ratio of profits of Rajan and Sajan = Ratio of their investments =14200 : 15600 = 142 : 156 = 71 : 78 ∴ Rajan's share = [71/(71 + 78)] x 74500 = (71/149) x 74500 = ₹ 35500

Question 13

In a partnership A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs. 4,600 B's share is?

Accepted Answer

Suppose A invests Rs. N/6 for M/ 6 months. B invests Rs. N/3 for M/3 months and C invests Rs. [N - (N/6 + N/3)] For M months. Ratio of their investment = (N/6 x M/6) : (N/3 x M/3) : (N / 2NM) = 1/36 : 1/9 : 1/2 = 1 : 4 : 18 ∴ B's share = Rs. 4600 x (4/23) = Rs. 800

Question 14

A, B and C entered into partnership by making investments in the ratio 3 : 5 : 7 After a year, C invests another Rs. 3,37,600 while A withdrew Rs. 45,600. The ratio of investment then changes to 24 : 59 : 167. How much did A invest initially?

Accepted Answer

Let initial investment be 3k, 5k and 7k rupees. ∵ (3k - 45600) : 5k : (7k + 337600) = 24 : 59 : 167 ⇒ (3k - 45600)/5k = 24/59 ∴ k = 47200 ∴ Initial investment of A = Rs. (47200 x 3) = Rs. 141600

Question 15

A and B entered into partnership A invests Rs. 16,000 for 8 months and B remains in the business for 4 months. Out of a total profit, B claims 2/7 of the profit. B contributed?

Accepted Answer

Ratio of profits of A and B = 5/7 : 2/7 = 5 : 2 ∵ (16000 x 8)/(N x 4) = 5/2 ⇒ 20N = 256000 ∴ N = 128000 So, B contributed Rs. 12800.

Question 16

A and B entered into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months. C joins of Rs. 21000. The share of B exceeds that of C, out of a total profit…

Accepted Answer

A : B : C = Rs. (16000 x 3 + 11000 x 9) : (12000 x 3 + 17000 x 9) : (21000 x 6) = 147 : 189 : 126 = 7 : 9 : 6 ∴ (B's share) - (C's share) = Rs. [ 26400 x (9/22) - 26400 x (6/22)] = Rs. (10800 - 7200) = Rs. 3600

Question 17

Kanti started a business investing Rs. 90000. Five months later Sudhakar joined him by investing Rs. 8000. If they make a profit of Rs. 6970 at the end of year. Sudhakar's share of profit is?

Accepted Answer

∵ Ratio of shares = (9000 x 12) : (8000 x 7) = 108 : 56 = 27 : 14 ∴ Sudhakar's share = Rs. 6970 x (14/41) = Rs. 2380

Question 18

A and B invest in a business in the ratio 3 : 2 if 5% of the total profit goes to charity and A's share is Rs. 855, total profit is?

Accepted Answer

Let the total profit be Rs. 100 After paying to Charity, A's share = Rs. 95 x (3/5) = Rs. 57 If A's share is Rs. 57, then total profit = Rs. 100 If A's share is Rs. 855, then total profit = Rs. 855 x (100/51) = Rs. 1500

Question 19

Sanjay and Komal started a business with Rs. 15000 each. After 8 months Komal withdrew Rs. 10000. If at the end of a year there was a profit of Rs. 32000. What was the share of Sanjay in the profit?

Accepted Answer

Sanjay's investment for 1 months = 15000 x 12 = Rs. 180000 Komal's investment for 1 months = 15000 x 8 + (15000 - 10000) x 4 = 120000 + 20000 = Rs. 140000 ∴ Ratio between the investment of Sanjay and Komal = 180000 : 140000 = 9 : 7 ∴ Sanjay's profit = [9/(9 + 7)] x 32000 = Rs. 18000

Question 20

A is a working and B is a sleeping partner in a business. A puts in Rs. 12,000 and B Rs. 20,000. A receives 10% of the profit for managing, the rest being divided in proportion to their capitals. Out of a total profit of Rs. 9600 the money received …

Accepted Answer

For management A receive = Rs. 960 Balance Amount = Rs. (9600 - 960) = Rs. 86400 Ratio of their investment = 12000 : 20000 = 3 : 5 ∴ A's share = Rs. 8640 x (3/8) = Rs. 3240 So, A receive = Rs. (3240 + 960) = Rs. 4200

Partnership Questions