A and B started a business by investing Rs. 75,000 and Rs. 45,000 respectively. After 3 months, C joined with Rs. 60,000. At the end of the year, what is C’s share in a profit of Rs. 40,000 (approx.)?

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

A: 75,000 × 12 = 9,00,000
B: 45,000 × 12 = 5,40,000
C joined after 3 months, so 9 months: 60,000 × 9 = 5,40,000

Ratio 9,00,000 : 5,40,000 : 5,40,000 = 5 : 3 : 3, total 11 parts
C's share = 3⁄11 × 40,000 = 10,909.09 ≈ Rs. 10,909 → option (a)

Why the others are wrong

• (b)
  Rs. 10,109 — Rs. 10,109 is about 25.3% of the profit, but C holds 3 of 11 parts, 27.3%. It is about 800 short of 3⁄11 × 40,000.
• (c)
  Rs. 15,909 — C and B have equal capital-months (5,40,000 each), so their shares are equal. Two shares of 15,909 would leave A 8,182, less than either, though A invested most.
• (d)
  Rs. 15,109 — Rs. 15,109 is more than a third of the profit (13,333). C holds 3 of 11 parts, under a third. Even counting C for all 12 months gives exactly a third.

In a partnership, each partner's profit is proportional to capital × time, because money that stays in the business longer earns for longer.

A partner who joins late counts the months after joining. C came in after 3 months of a 12-month year, so C's money worked for 9 months.

Equal capital-months mean equal shares: C's 60,000 for 9 months matches B's 45,000 for 12.

Key facts

• Profit ratio = ratio of capital × months for each partner.
• A partner joining after m months of a 12-month year has invested for 12 − m months.
• Here the ratio is 5 : 3 : 3, so A gets 5⁄11 (about Rs. 18,182) and B and C get 3⁄11 each (about Rs. 10,909).

Common traps

• Counting C for the full 12 months: that makes the ratio 5 : 3 : 4 and C's share Rs. 13,333.
• Using 3 months for C because the stem says "after 3 months": 3 is the delay, not the time invested.

No directly related past PYQ was found.