A and B start a business jointly. A invests Rs. 16,000 for 8 months and B…

In a partnership, when partners invest for different durations, profit is shared in the ratio of each partner's capital multiplied by the time for which it remained invested (investment times time), not in the raw investment ratio alone.

1. A's investment-time product = 16,000 times 8 = 1,28,000.

2. B's share of profit is 2/7, so A's share is 1 minus 2/7 = 5/7; therefore the profit ratio A : B = 5 : 2.

3. Let B's contribution be x. B's investment-time product = x times 4.

4. Equate the investment-time ratio to the profit ratio: (16,000 times 8) : (x times 4) = 5 : 2, that is, 1,28,000 / 4x = 5/2.

5. Cross-multiply: 1,28,000 times 2 = 5 times 4x, so 2,56,000 = 20x, giving x = 12,800.

Check: if B invests Rs. 12,800 for 4 months, B's investment-time product is 12,800 times 4 = 51,200. The ratio 1,28,000 : 51,200 simplifies to 5 : 2, confirming B's profit share works out to 2 divided by (5 plus 2) = 2/7, matching the given condition.