Amit and Ravi invested capitals in the ratio 5:4. At the end of 8 months Amit…

In a partnership, each partner's profit share is proportional to the product of the capital invested and the time for which it stays invested (Capital × Time). When two partners' profits come out equal, their capital-time products must be equal: Capital1 × Time1 = Capital2 × Time2.

1. Let Amit's capital = 5k and Ravi's capital = 4k, since the capitals are in the ratio 5:4.

2. Amit's investment duration is Time1 = 8 months (given).

3. Let Ravi's investment duration be Time2 months (to find).

4. Since the profits are equal, Capital1 × Time1 = Capital2 × Time2: 5k × 8 = 4k × Time2.

5. Simplify: 40k = 4k × Time2, so Time2 = 40k / 4k = 10.

Cross-check: Amit's capital-time product is 5 × 8 = 40 (in units of k), and Ravi's is 4 × 10 = 40 — equal, confirming the profits indeed come out the same.

Hence, Ravi invested his money for 10 months.