25. 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?

1. A. ₹ 30,000
2. B. ₹ 26,000
3. C. ₹ 24,000
4. D. ₹ 20,000

Answer: A

Explanation

Let Q’s capital be ₹X. Then P’s capital is ₹(X + 14000). P invested for 8 months, and Q for 10 months. The total profit is ₹2000. P’s share is ₹400 more than Q’s share. Let Q’s profit share be ₹Y. Then P’s profit share is ₹(Y + 400). Total profit = Y + (Y + 400) = 2Y + 400 = 2000. Solving for Y, 2Y = 1600, so Y = 800. Thus, Q’s profit share is ₹800, and P’s profit share is ₹1200. In a partnership, profit is distributed in the ratio of (Capital × Time). So, (P’s Capital × P’s Time) / (Q’s Capital × Q’s Time) = P’s Profit / Q’s Profit. ( (X + 14000) × 8 ) / ( X × 10 ) = 1200 / 800. Simplifying, (8X + 112000) / 10X = 3/2. Cross-multiplying: 2(8X + 112000) = 3(10X) => 16X + 224000 = 30X. This gives 14X = 224000, so X = 16000. Q’s capital is ₹16000. P’s capital = X + 14000 = 16000 + 14000 = ₹30000. This question tests the concept of partnership and profit distribution based on capital and time invested.