A and B start a business with investments of Rs. 5000 and Rs. 4500 respectively. After 4 months, A takes out half of his capital. After two more months, B takes out one-third of his capital while C joins them with a capital of Rs. 7000. At the end of a year, they earn a profit of Rs. 5080. Find the share of each member in the profit.

Options

A. A-Rs. 1400, B - Rs. 1900, C- Rs. 1780
B. A-Rs. 1600, B - Rs. 1800, C- Rs. 1680
C. A-Rs. 1800, B - Rs. 1500, C- Rs. 1780
D. A-Rs. 1680, B - Rs. 1600, C- Rs. 1800

Answer

To solve the problem step by step, we will calculate the effective capital contribution of each partner over the year and then determine their share of the profit based on these contributions.

### Step 1: Calculate A's Contribution
- A's initial investment = Rs. 5000
- A invests this amount for the first 4 months.
- After 4 months, A withdraws half of his capital, which is Rs. 2500.
- Therefore, A's remaining capital = Rs. 2500.
- A's contribution for the first 4 months = 5000 * 4 = Rs. 20000
- A's contribution for the next 8 months (after withdrawing half) = 2500 * 8 = Rs. 20000
- Total contribution of A = Rs. 20000 + Rs. 20000 = Rs. 40000

### Step 2: Calculate B's Contribution
- B's initial investment = Rs. 4500
- B invests this amount for the first 6 months.
- After 6 months, B withdraws one-third of his capital, which is Rs. 1500.
- Therefore, B's remaining capital = Rs. 4500 - Rs. 1500 = Rs. 3000.
- B's contribution for the first 6 months = 4500 * 6 = Rs. 27000
- B's contribution for the next 6 months (after withdrawing one-third) = 3000 * 6 = Rs. 18000
- Total contribution of B = Rs. 27000 + Rs. 18000 = Rs. 45000

### Step 3: Calculate C's Contribution
- C joins the business with an investment of Rs. 7000 for the last 6 months.
- C's contribution for these 6 months = 7000 * 6 = Rs. 42000

### Step 4: Calculate Total Contributions
- Total contribution of A = Rs. 40000
- Total contribution of B = Rs. 45000
- Total contribution of C = Rs. 42000
- Total contributions = Rs. 40000 + Rs. 45000 + Rs. 42000 = Rs. 127000

### Step 5: Calculate Profit Shares
- Total profit = Rs. 5080
- A's share of profit = (A's contribution / Total contributions) * Total profit
- A's share = (40000 / 127000) * 5080 = Rs. 1600
- B's share of profit = (B's contribution / Total contributions) * Total profit
- B's share = (45000 / 127000) * 5080 = Rs. 1800
- C's share of profit = (C's contribution / Total contributions) * Total profit
- C's share = (42000 / 127000) * 5080 = Rs. 1680

### Step 6: Final Shares
- A's share = Rs. 1600
- B's share = Rs. 1800
- C's share = Rs. 1680

### Summary of Shares
- A: Rs. 1600
- B: Rs. 1800
- C: Rs. 1680