If the ratio of capital of A and B is 3:2 and the time for which they invested is in the ratio 2:3, then the profit ratio is:

Correct — A. Partners share profit in the ratio of capital × time.

A: capital × time = 3 × 2 = 6
B: capital × time = 2 × 3 = 6

Profit ratio = 6 : 6 = 1 : 1 → option (a)

Why the others are wrong

• (b)
  2:1 — 2 : 1 would need A's capital × time to be double B's. Both products are 6, so neither partner earns more than the other.
• (c)
  3:2 — 3 : 2 is the capital ratio alone. It ignores that B stayed 3 units of time to A's 2, which exactly offsets A's larger capital.
• (d)
  3:1 — 3 : 1 matches neither product. A's larger capital (3 against 2) is cancelled by A's shorter time (2 against 3), so A cannot earn three times B's share.

A partner's claim on profit grows with how much is invested and for how long. So each partner's weight is capital × time, and profit is split in the ratio of those products.

Here the two ratios are reverses of each other, 3 : 2 and 2 : 3. Reversed ratios always give equal products (3 × 2 = 2 × 3), so the profit splits equally.

Key facts

• Profit ratio = (A's capital × A's time) : (B's capital × B's time).
• When the times are equal, profit follows the capital ratio alone.
• When the capitals are equal, profit follows the time ratio alone.

Common traps

• Stopping at the capital ratio, 3 : 2, and forgetting to multiply by time.
• Dividing capital by time instead of multiplying: 3⁄2 : 2⁄3 gives 9 : 4, which is not the rule.

No directly related past PYQ was found.