# Partnership – Solved Aptitude Questions

(01) A and B rent pasture for 10 months. A puts 100 cows for 8 months. How many cows can B put for the remaining two months. If he pays 3/2 as much as A pays?

Sol. Given: Time of pasture rent by A and B =10 months

A = 100 cows which can be treated as his capital for time = 8 months

To find: B = no. of cows I.e. His capital for time = 2 months

According to the question, the ratio of profit is 2/3

As we know that Capital x Time = Profit

Therefore, A/B = (100 x 8)/ (C2 x 2) = 2/3

C2 = (100 x 8 x 3)/ (2 x 2)

= 2400/ 4

= 600

Ans. B has 600 cows for pasture.

(02) A & B started a business with Rs. 50,000 & 20,000. A is working partner and takes 20% of the total profit as his salary and remaining profit is divided according to their capital. If in this process A received Rs. 38000 more than B. Find the amount of total profit.

Sol. Given: Capital of A = Rs. 50,000 and B = Rs. 20,000

Ratio of their Capitals = 50,000: 20,000 = 5: 2

A’s Salary = (1/ A’s ratio of capital) x (Sum of their Capital)

= (1/5) x 7

= 1.4

Profit for sharing = Sum of their Capital ratio- A’s Salary ratio

= 7 – 1.4

= 5.6

Now, A’s part = A’s salary ratio + (Ratio of A/ Sum of their ratio capital) x Profit for sharing

= 1.4 + [(5/7) x 5.6]

= 5.4

B’s part = (ratio of B/ Sum of ratio of their capital) = (2/7) x 5.6 = 1.6

According to the question, A’s part – B’s part = 38000

5.4 – 1.6 = 38000

3.8    = 38000

1 unit   = 38000/ 3.8 = 10,000

Therefore, total profit   = 10,000 x (Sum of their capital ratio)

= 10,000 x 7

= Rs. 70,000

Ans. The total profit amount is Rs. 70,000

(03) A puts Rs. 375 more in a business than B. A invest for 8 months while B for 4 months. If the share of A is 75 more than that of B out of total profit of Rs. 125. Find the capital invested by A.

Sol. Given: Time of A’s investment = 8 months while that of B’s = 4 months

Total profit = Rs.125

Out of A’s profit = Rs. 100

And B’s     = Rs. 25    (As conditions according to the question)

Ratio of their Profit = 100: 25 = 4:1

Ratio of their time = 8:4 = 2:1

As we know that, C x T = P

Therefore,    C = P/T

C1 = 4/ 2 = 2 and C2 = 1/1

Hence ratio of their Capital = 2

Since A puts 375 more than B, therefore (2 – 1) = 375

1 unit = 375

Capital invested by A = 375 x (Ratio of A’s capital) = 375 x 2 = Rs. 750

Ans. A’s capital is 750

(04) A, B and C are three partners A received 5/8 part of total profit & remaining profit received by B and C equally. A’s income is increased by Rs. 450 when the profit rises from 4% to 9%. Find the capital invested by B & C each.

Sol. Given: A’s profit = 5/8

Remaining profit = 1 – 5/8 = 3/8 (which is distributed between B and C equally)

Now, let us assume the total Capital to be Rs. 100

Profit of A = 4 % = 4 x (5/8) = 20/ 8

Profit of A = 9 % = 9 x (5/8) = 45/ 8

According to the question, 45/ 8 – 20/ 8 = 450

25/ 8 units = 450

1 unit = 450 x (8/ 25)

100 units = 450 x (8/ 25) x 100

Total profit = Rs. 14,400

Again given: Ratio of their profit = A : (B + C) = 5: 3

Therefore, B + C = (3/8) x 14400 = Rs. 5400

B = C = 5400/ 2 = Rs. 2700

Ans. Therefore B and C invested Rs. 2700 each.

(05) A, B and C are three partners. A gets 2/7 part of total profit. B & C share the remaining profit equally. A’s income increases by Rs. 240 when profit rise from 10% to 15%. Find the capital invested by B & C.

Sol. Given: A’s profit = 2/7

Remaining profit = 1 – 2/7 = 5/7 (which is distributed between B and C equally)

Now, let us assume the total Capital to be Rs. 100

Profit of A = 10 % = 10 x (2/7) = 20/7

Profit of A = 15% = 15 x (2/7) = 30/7

According to the question, 30/ 7 – 20/ 7 = 240

10/7 units = 240

1 unit = 240 x (7/ 10)

100 units = 240 x (7/ 10) x 100

Total profit = Rs. 16,800

Again given: Ratio of their profit = A : (B + C) = 2: 5

Therefore, B + C = (5/7) x 16800 = Rs. 12000

B = C = 5400/ 2 = Rs. 6000

Ans. Therefore B and C invested Rs. 6000 each.

(06) A, B and C invested money in the ratio of 1/ 2 : 1/ 3: 1/ 5 in a business. After 4 months A doubled his investment and after 6 months B, half his investment. If the total profit at the end of year be 34650 then find the share of each in profit.

Sol. Given: Ratio of capital invested by A, B and C = 1/ 2: 1/ 3: 1/ 5

Which can be simplified as 15: 10: 6   (solving by L.C.M. method)

Let the unit of unit capital invested by A is x

According to the question, total capital invested by A in 1 year = 15x. 4 + (15x.2).8

= 60x + 240x = 300x

Total capital invested by B in 1 year = 10x.6 + (10x/ 2).6 = 60x + 30x = 90x

Total capital invested by C in 1 year = 6x. 12 = 72x

Ratio of their profits = 300x : 90x : 72x   (dividing by 6)

= 50x: 15x: 12x

Again according to the question, 50x + 15x + 12x = 34650

77x         = 34650

x          = 34650/ 77 = Rs. 450

Ans       Profit of A = 50x = 50. 450 = Rs. 22500

Profit of B = 15x = 15. 450 = Rs. 6750

Profit of C = 12x = 12. 450 = Rs. 5400

(07) A and B started a business by investing 36000 and 45000 respectively. After 4 months B withdraws 4/ 9 of his investment. its 5 months after she again invested 11/ 9 of its original investment. If the total earned profit at the end of the year, is 117240, then who will get more money as a share of profit and how much?

Sol. Given: Capital of A = Rs. 36000 and that of B = Rs. 45000

Total capital invested by A at the end of year =36000 x 12 = Rs. 432000

Total capital invested by B at the end of year

= 45000 x 4 + (45000 – (4/ 9). 45000) x 5 + [(11/ 9). 45000 + (4/ 9). 45000 )] x 3

= 45000 x 4 + (45000 – 20000) x 5 + [55000 + 25000] x 3

= 180000 + 125000 + 240000

= 545000

Ratio of their profit = 432000: 545000 = 432 : 545

(432 + 545)x = 117240

977 x =  117240

1 x = 117240/ 977 = 120

Difference in their profit = (545 – 432) x 120 = 113 x 120 = 13560

Ans. B will get Rs. 13560 more than A.

(08) A & B start A business, A invests 1/4 capital for 1/4th time and B invests 1/5th capital for 1/2 time and C invests the remaining capital for full time. How should they divide the profit of Rs 1140?

Sol. Let us consider the capital to be 20 if the time to be consider is 1 year then

Time for A = (1/ 4) x 12 = 3 months while capital = (1/ 4) x 20 = 5

Time for B = (1/ 2) x 12 = 6 months while capital = (1/ 5) x 20 = 4

Time for C = 12 months while capital = 20 – (5 + 4) = 11

As we know that capital x time = profit

Therefore their profit ratio = 5×3: 4×6: 11×12 = 15: 24:132

= 5: 8: 44 (dividing by 3)

Ans. Hence they should divide the profit in the ratio of 5: 8: 44

(09) In a partnership business, B’s capital was half of A’s. If after 8 months. B withdrew half of his capital and after 2 months more A withdrew 1/4th of his capital, then the profit ratio of A and B will be:

Sol. Given: 2 x B’s capital = A’s capital

Therefore their capital ratio = A : B = 2: 1  (Let us consider the unit to be 100 I.e., 200: 100)

As we know that Capital x time = Profit

Then According to the question, Profit of A = 200 x 10 + (3/ 4) x 200 x 2 (1 – 1/ 4 = 3/ 4)

= 2000 + 300

= 2300

Profit of B      = 100 x 8 + (1/ 2) x 100 x 4

= 800 + 200

= Rs. 1000

Ans. The ratio of their profit will be 2300: 1000 = 23: 10

(10) A and B invest in the ratio 3 : 5. After 6 months, C joins the business investing an amount equal to B’s. At the end of the year what will be the ratio of their profits?

Sol. Given: Ratio of capital of A and B = 3: 5  (Let us consider the unit to be 100 I.e., 300: 500)

As we know that Capital x time = Profit

Then According to the question, Profit of A = 300 x 12 = Rs. 3600

Profit of B = 500 x 12 = Rs. 60000

Profit of C = 500 x 6 = Rs. 3000

Ratio of Profits = 3600: 60000 : 3000

= 6: 10: 5

Ans. The required ratio is 6: 10: 5