Abdul and Mohsin together invested ₹56,000 in a business. At the end of the…

Concept

When two or more partners invest capital for the SAME time period, the total profit is divided in exact proportion to their investments. This works both ways: if the profit shares are known, the ratio of the shares directly gives the ratio of the investments.

Application

1. Total profit = ₹16,000 and Mohsin's share = ₹2,700, so Abdul's share = 16,000 − 2,700 = ₹13,300.

2. Since profit is shared in the ratio of investment, Mohsin : Abdul (investment) = Mohsin : Abdul (profit share) = 2,700 : 13,300.

3. Dividing both terms by their HCF (100) gives the ratio in lowest terms: 2,700 : 13,300 = 27 : 133.

4. Sum of the ratio parts = 27 + 133 = 160, and this represents the total investment of ₹56,000, so 1 part = 56,000 ÷ 160 = ₹350.

5. Mohsin's investment = 27 × 350 = ₹9,450.

6. Abdul's investment = 133 × 350 = ₹46,550.

7. Difference of their investments = 46,550 − 9,450 = ₹37,100.

Cross-check

The two investments add up to 9,450 + 46,550 = ₹56,000, matching the given total. Also, Mohsin's profit share works out to 16,000 × (27 ÷ 160) = ₹2,700, exactly matching the given data, confirming the ratio is correct.

So the difference between Abdul's and Mohsin's investments is ₹37,100.