Question

A and B start a business with capitals of ₹50,000 and ₹40,000 respectively. After 6 months, C joins them with ₹80,000. Find the share of each in a profit of ₹25,000 at the end of the year.

Hint:

In partnership problems always use the formula: \[ \text{Profit share} \propto \text{Capital} \times \text{Time}. \] First compute the capital–time product for each partner, form the ratio, and then divide the total profit accordingly.

Answer 1

Concept: In partnership problems, profit is divided in the ratio of capital × time. Thus, each partner’s share depends on the amount of money invested and the duration for which it was invested. \[ \text{Profit ratio} \propto (\text{Capital} \times \text{Time}) \]
Step 1: Calculate capital–time product for each partner. \[ A: 50,000 \times 12 = 600,000 \] \[ B: 40,000 \times 12 = 480,000 \] C joins after 6 months: \[ C: 80,000 \times 6 = 480,000 \]
Step 2: Find the ratio of their investments. \[ A:B:C = 600,000 : 480,000 : 480,000 \] Dividing by \(120,000\): \[ A:B:C = 5:4:4 \]
Step 3: Divide the total profit according to the ratio. Total ratio parts: \[ 5+4+4=13 \] Total profit = ₹25,000 \[ \text{Value of one part}=\frac{25000}{13} \]
Step 4: Calculate individual shares. \[ A=\frac{5}{13}\times 25000=\frac{125000}{13}\approx ₹9615.38 \] \[ B=\frac{4}{13}\times 25000=\frac{100000}{13}\approx ₹7692.31 \] \[ C=\frac{4}{13}\times 25000=\frac{100000}{13}\approx ₹7692.31 \]
Step 5: Final distribution of profit. \[ A = ₹9615.38,\quad B = ₹7692.31,\quad C = ₹7692.31 \]