Abdul and Mohsin together invested ₹31,700 in a business. At the end of the…

In a partnership where both partners invest for the same length of time, profit is divided directly in proportion to the capital each one invested — Investment(A) : Investment(B) equals Profit(A) : Profit(B). So once the profit-sharing ratio between two partners is known, the same ratio splits any known combined investment into each partner's own share.

1. Total profit is ₹17,500 and Mohsin's share of it is ₹7,000, so Abdul's share of the profit is 17,500 − 7,000 = ₹10,500.

2. Because both partners invested for the same period, the investment ratio equals the profit ratio: Abdul : Mohsin = 10,500 : 7,000.

3. Simplify the ratio by dividing both terms by their common factor 3,500: 10,500 : 7,000 = 3 : 2.

4. The combined investment of ₹31,700 corresponds to 3 + 2 = 5 equal parts, so one part = 31,700 ÷ 5 = ₹6,340.

5. Abdul's investment = 3 × 6,340 = ₹19,020; Mohsin's investment = 2 × 6,340 = ₹12,680.

6. Difference of their investments = 19,020 − 12,680 = ₹6,340.

Cross-check: 19,020 + 12,680 = 31,700, which matches the total investment. Splitting the profit of ₹17,500 in the same 3 : 2 ratio gives Abdul (3/5) × 17,500 = ₹10,500 and Mohsin (2/5) × 17,500 = ₹7,000, which matches the amounts stated in the question. So the difference between their investments is ₹6,340.