Three partners P, Q and R invested their amounts in the ratio 2 : 5 : 7. At…

Concept

In a partnership, each partner's share of profit is proportional to their capital-months — the amount invested multiplied by the number of months it stayed in the business. When a partner changes their capital part-way through, you sum the capital-months for each separate period.

Application

1. Take the initial investments in the ratio 2 : 5 : 7, so P = 2, Q = 5 and R = 7 units.

2. Q and R keep their amounts for the whole 12 months. P changes after 6 months: the new amount equals half the sum of Q's and R's initial investment = (5 + 7) / 2 = 6 units.

3. Capital-months for P = (2 x 6) + (6 x 6) = 12 + 36 = 48.

4. Capital-months for Q = 5 x 12 = 60.

5. Capital-months for R = 7 x 12 = 84.

6. Profit is shared in the capital-months ratio P : Q : R = 48 : 60 : 84, a total of 48 + 60 + 84 = 192 parts (this ratio simplifies to 4 : 5 : 7, but we keep the 192-part form to match Q's 60 parts directly).

7. Q's 60 parts equal Rs 425, so one part = 425 / 60. Total profit = 192 parts = 425 x (192 / 60) = Rs 1360.

Cross-check

Split Rs 1360 in the ratio 48 : 60 : 84 (one part = 1360 / 192 = 7.0833): P gets 48 parts = Rs 340, Q gets 60 parts = Rs 425, R gets 84 parts = Rs 595. Q's share matches the given Rs 425, confirming the total of Rs 1360.