Gautam started a business with a sum of ₹ 60,000. Jatin joined him 8 months later with a sum of ₹ 35,000. At what respective ratio will the two share the profit after two years?

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

Gautam's time: two years = 24 months
Jatin's time: 24 − 8 = 16 months
Products, in ₹000 × months: 60 × 24 = 1440 and 35 × 16 = 560

Divide both by 80: 1440 : 560 = 18 : 7 → option (a)

Why the others are wrong

• (b)
  15:7 — 15:7 equals 1200 : 560, which would mean Gautam's ₹60,000 worked for only 20 months (1200 ÷ 60). He was in the business for all 24.
• (c)
  12:7 — 12:7 is 60,000 : 35,000, the capitals alone. It ignores that Jatin's money was in for 16 months against Gautam's 24.
• (d)
  5:7 — 5:7 gives Jatin the larger share, yet he put in less money (₹35,000 against ₹60,000) for less time (16 months against 24).

In a partnership each partner's claim on the profit is capital multiplied by the months it was invested. The same money kept in for longer earns a larger share.

A late joiner's time is the total period minus the months he waited. Two years is 24 months, so Jatin's ₹35,000 counts for 16 of them.

Key facts

• Profit ratio = (capital₁ × time₁) : (capital₂ × time₂).
• A partner who joins m months late is invested for (total months − m).
• Capital ratio 12 : 7 times time ratio 3 : 2 gives 36 : 14 = 18 : 7.

Common traps

• Using Jatin's 8 waiting months as his invested time: 60 × 24 : 35 × 8 = 36 : 7.
• Dividing the profit by capital alone, which gives 12:7.

No directly related past PYQ was found.