Question

In a partnership, A invests one-fourth of the capital for one-third of the time, B invests one-third of the capital for one-fourth of the time and C invests the rest of the capital for the whole time. Out of a profit of ₹3,500, A's share is:

• A. ₹1,000
• B. ₹1,500
• C. ₹500
• D. ₹2,500

Answer 1

The Correct Option is C

To determine A's share of the profit, we use the concept of profit sharing in partnership based on the capital contributed and the duration of time for which the capital is invested. Let's assign variables for the total capital and duration:

Let the total capital be 1 unit and time be T units.

A's contribution is one-fourth of the capital for one-third of the time, so A's effective investment is: (1/4) * (1/3) * T = T/12

B's contribution is one-third of the capital for one-fourth of the time, so B's effective investment is: (1/3) * (1/4) * T = T/12

C invests the remaining capital, which is: 1 − (1/4 + 1/3) = 1 − 7/12 = 5/12 for the entire time, so C's effective investment is: (5/12) * T = 5T/12

Now, compute the ratio of their investments:

A : B : C = T/12 : T/12 : 5T/12 = 1 : 1 : 5

The total profit of ₹3,500 is to be divided in this ratio. The sum of the shares is: 1 + 1 + 5 = 7

A's share of the profit = (1/7) * ₹3,500 = ₹500