A and B start a business. A invests ₹80,000 for 9 months, B invests ₹1,20,000 for 6 months. What is B’s share of a ₹45,000 profit?

Correct — D. Profit is shared in the ratio of capital × months.

A: 80,000 × 9 = 7,20,000
B: 1,20,000 × 6 = 7,20,000
Ratio A : B = 1 : 1, so the profit halves
B = 45,000 ÷ 2 = ₹22,500 → option (d)

Why the others are wrong

• (a)
  ₹26,500 — ₹26,500 leaves A ₹18,500, so B would get more than A. But their capital-months are equal, 7,20,000 each, so the shares must be equal too.
• (b)
  ₹28,000 — ₹28,000 leaves A only ₹17,000. B's larger capital is cancelled by A's longer time, so B cannot take more than half.
• (c)
  ₹36,000 — ₹36,000 is four-fifths of the profit, a 4 : 1 split in B's favour. Neither the capital ratio (2 : 3) nor the time ratio (3 : 2) comes close to that.

Profit follows capital × time, not either one alone.

B brings more money, 1,20,000 against 80,000, a 2 : 3 capital ratio. A keeps his money in longer, 9 months against 6, a 3 : 2 time ratio.

Multiply the two ratios: 2 × 3 : 3 × 2 = 6 : 6 = 1 : 1. The two advantages cancel exactly, so the profit splits evenly.

Key facts

• Each partner's share is proportional to capital × time.
• 80,000 × 9 = 1,20,000 × 6 = 7,20,000.
• A capital ratio of 2 : 3 times a time ratio of 3 : 2 gives 1 : 1.

Common traps

• Splitting by capital alone (2 : 3), which gives B ₹27,000.
• Splitting by time alone (3 : 2), which gives B ₹18,000.

No directly related past PYQ was found.