A starts a business with Rs. 3500 and after 5 months, B joins with A as his…

In a partnership, when partners invest different capitals for different time periods, the profit is shared in the ratio of the products of each partner's capital and the time for which it was invested — that is, Profit Ratio = (Capital of A × Time of A) : (Capital of B × Time of B).

1. A invests Rs. 3500 for the entire year, i.e., for 12 months.

2. B joins as a partner after 5 months, so B's capital remains invested for the remaining 12 − 5 = 7 months.

3. Let B's capital be Rs. P. By the partnership rule, the profit ratio is (3500 × 12) : (P × 7).

4. This given profit ratio is 2 : 3, so (3500 × 12) : (P × 7) = 2 : 3.

5. Cross-multiplying: 3 × 3500 × 12 = 2 × P × 7.

6. Simplify: 126000 = 14 × P, so P = 126000 ÷ 14 = 9000.

Checking back: (3500 × 12) : (9000 × 7) = 42000 : 63000, which simplifies to 2 : 3 — exactly the given ratio, confirming B's capital contribution is Rs. 9000.