A, B and C enter into a partnership with a capital in which A's contribution…

In a partnership, when all partners' capitals are invested for the same time period, the ratio in which they share profit is exactly the ratio of their capitals. So once the profit-sharing ratio is known, every partner's capital can be found by scaling that ratio against any one partner's known capital.

1. Total profit is Rs. 1000. A gets Rs. 500 and B gets Rs. 300.

2. C's share of profit = 1000 - (500 + 300) = Rs. 200.

3. The profit-sharing ratio A : B : C = 500 : 300 : 200 = 5 : 3 : 2.

4. Since capital is proportional to profit share, A's capital of Rs. 10,000 corresponds to ratio part 5.

5. Value of one ratio part = 10,000 / 5 = Rs. 2,000.

6. C's capital corresponds to ratio part 2, so C's capital = 2 x 2,000 = Rs. 4,000.

Cross-check: total capital = (5 + 3 + 2) x 2,000 = Rs. 20,000, giving A : B : C capitals as 10,000 : 6,000 : 4,000 -- a ratio of 5 : 3 : 2, matching the profit ratio and confirming C's capital is Rs. 4,000.