A and B enter into a partnership and invest Rs. 12,000 and Rs. 16,000…

Concept: When partners invest different amounts of capital for different durations in a partnership, profit is shared in proportion to each partner's capital multiplied by the number of months that capital stayed invested (the capital times time, or equivalent-capital, method). A partner who joins partway through the venture is weighted only for the months actually invested, not the full duration of the partnership.

Application:

1. The total duration of the partnership is 2 years = 24 months.

2. A invested Rs. 12,000 for the full 24 months, so A's weight = 12,000 x 24 = 2,88,000.

3. B invested Rs. 16,000 for the full 24 months, so B's weight = 16,000 x 24 = 3,84,000.

4. C joined after 8 months, so C's capital of Rs. 15,000 stayed invested for 24 minus 8 = 16 months, giving a weight of 15,000 x 16 = 2,40,000.

5. Combined weight of all three partners = 2,88,000 + 3,84,000 + 2,40,000 = 9,12,000.

6. C's share of the profit = (C's weight divided by combined weight) x total profit = (2,40,000 divided by 9,12,000) x 45,600 = Rs. 12,000.

Cross-check: Computing the other two shares the same way, A gets (2,88,000 divided by 9,12,000) x 45,600 = Rs. 14,400 and B gets (3,84,000 divided by 9,12,000) x 45,600 = Rs. 19,200. Adding all three shares, 14,400 + 19,200 + 12,000 = 45,600, which matches the total profit exactly, confirming the split.

Result: C's share of the profit is Rs. 12,000.