Question 1

Two partners, X and Y, start a business with capital in the ratio 5:7. After 6 months, X withdraws half of his capital and Y adds ₹2,000 more. If the profit at the end of the year is ₹2,640, what is X's profit share?

Accepted Answer

Step 1: Let X's initial capital = 5k and Y's initial capital = 7k. Step 2: X's capital × time = 5k × 6 + 2.5k × 6 = 45k. Y's capital × time = 7k × 6 + (7k + 2,000) × 6 = 84k + 12,000. Step 3: Assume k = 1,000 for clean calculation. X = 45,000, Y = 96,000. Step 4: Ratio = 45,000 : 96,000 = 15 : 32. Step 5: Total parts = 47. X's share = (15/47) × 2,640 = ₹840.

Question 2

Three partners A, B, and C invest in a business in the ratio 3:4:5. After 1 year, the profit is ₹3,600. If A's profit share is ₹900, what is C's profit share?

Accepted Answer

Step 1: The profit is distributed in the same ratio as the investments (assuming equal time period). Ratio A:B:C = 3:4:5. Step 2: Total parts = 3 + 4 + 5 = 12. Step 3: A's share = (3/12) × Total Profit. Given A's share = ₹900. Step 4: 900 = (3/12) × Total Profit. Total Profit = 900 × 12/3 = 3,600. (This confirms the given profit.) Step 5: C's share = (5/12) × 3,600 = ₹1,500.

Question 3

M and N enter into a partnership. M invests ₹15,000 for the entire year, while N invests ₹20,000 for 9 months. At the end of the year, the profit is ₹5,200. How much more profit does M earn compared to N?

Accepted Answer

Step 1: Calculate capital × time for each partner. M: 15,000 × 12 = 180,000. N: 20,000 × 9 = 180,000. Step 2: Ratio M:N = 180,000 : 180,000 = 1:1. Step 3: Total parts = 2. Step 4: M's share = (1/2) × 5,200 = ₹2,600. N's share = (1/2) × 5,200 = ₹2,600. Step 5: Difference = 2,600 - 2,600 = ₹0.

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