Two persons P and Q enter into a business. P puts ₹14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share is ₹400 more than Q’s share out of the total profit of ₹2,000, what is the capital contributed by P?
Answer & explanation
Answer: (a) ₹30,000
Out of ₹2,000, P gets ₹1,200 and Q ₹800, a ratio of 3 : 2. Profit is shared in the ratio of capital × time, so 8(Q + 14,000) : 10Q = 3 : 2, which gives Q = ₹16,000 and P = ₹30,000.
- Shares add to 2,000 and differ by 400, so P gets ₹1,200 and Q ₹800; ratio 3 : 2.
- Let Q’s capital be x; then P’s capital is x + 14,000.
- 8(x + 14,000) : 10x = 3 : 2 → 16(x + 14,000) = 30x → 14x = 2,24,000 → x = 16,000.
- P’s capital = 16,000 + 14,000 = ₹30,000.
- Check: 30,000 × 8 = 2,40,000 and 16,000 × 10 = 1,60,000, a ratio of 3 : 2.
Remember · Profit share is proportional to capital × time. Turn the profit clue into a ratio first, then solve one equation.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·