A starts a business with Rs. 50,000. B invests Rs. 40,000 at the same time. After 4 months, B increases his investment by Rs. 10,000. After 6 months from the start, C joins with Rs. 60,000. The business runs for 1 year and the total profit at the end is Rs. 1,90,000. Find B’s share in the profit.

Solution

ATQ, Compute “capital × time” for each partner (in month-rupees). Total time = 12 months. A: 50,000 for 12 months ⇒ A’s capital-months = 50,000 × 12 = 600,000. B: First 4 months: 40,000 Next 8 months: 50,000 ⇒ B’s capital-months = 40,000 × 4 + 50,000 × 8 = 160,000 + 400,000 = 560,000. C: Joins after 6 months, so invests for 6 months: 60,000 × 6 = 360,000. So ratio of their capitals (in terms of 10,000-month units): A : B : C = 600,000 : 560,000 : 360,000 Divide by 40,000: = 15 : 14 : 9. Total parts = 15 + 14 + 9 = 38. B’s share = (14/38) × 1,90,000. Compute: 1,90,000 ÷ 38 = 5,000. ⇒ B’s share = 5,000 × 14 = Rs. 70,000. Answer: B’s share in the profit = Rs. 70,000.