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?
- (a) ₹ 30,000 ✓ UPSC's answer
- (b) ₹ 26,000
- (c) ₹ 24,000
- (d) ₹ 20,000
Why the answer is (a)
• Let Q's capital be x, so P's capital is x + 14,000.
• The profit sharing ratio is determined by the product of capital and time: P's share is proportional to 8(x + 14,000) and Q's share is proportional to 10x.
• The total profit is ₹2,000, and P's share is ₹400 more than Q's share, meaning P gets ₹1,200 and Q gets ₹800.
• The ratio of their shares is 1,200 : 800, which simplifies to 3 : 2.
• Equating the profit ratio to the investment-time ratio: 8(x + 14,000) / 10x = 3 / 2.
• Solving the equation 16(x + 14,000) = 30x gives 16x + 224,000 = 30x, so 14x = 224,000, resulting in x = 16,000.
• Therefore, P's capital is x + 14,000 = 16,000 + 14,000 = ₹30,000.
Why the other options are wrong
- (b) ₹ 26,000
- ₹26,000 implies Q's capital is ₹12,000, which results in a profit ratio of 104:120 (13:15), not the required 3:2.
- (c) ₹ 24,000
- ₹24,000 implies Q's capital is ₹10,000, which results in a profit ratio of 96:100 (24:25), not the required 3:2.
- (d) ₹ 20,000
- ₹20,000 implies Q's capital is ₹6,000, which results in a profit ratio of 80:60 (4:3), not the required 3:2.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.