A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A ?

Options

A. A) Rs. 240
B. B) Rs. 75
C. C) Rs. 125
D. D) Rs. 354

Answer

To find the share of A in the profit, we will follow these steps:

### Step 1: Determine the initial investments of A and B.
- A's initial investment = Rs. 3000
- B's initial investment = Rs. 4000

### Step 2: Calculate the contribution of A and B for the first 8 months.
- A's contribution for 8 months = Rs. 3000 * 8 = Rs. 24000
- B's contribution for 8 months = Rs. 4000 * 8 = Rs. 32000

### Step 3: Adjust the investments after 8 months.
- After 8 months, A withdraws Rs. 1000, so A's new investment = Rs. 3000 - Rs. 1000 = Rs. 2000.
- B adds Rs. 1000, so B's new investment = Rs. 4000 + Rs. 1000 = Rs. 5000.

### Step 4: Calculate the contribution of A and B for the remaining 4 months.
- A's contribution for the remaining 4 months = Rs. 2000 * 4 = Rs. 8000
- B's contribution for the remaining 4 months = Rs. 5000 * 4 = Rs. 20000

### Step 5: Calculate the total contributions of A and B.
- Total contribution of A = Contribution for first 8 months + Contribution for last 4 months
- Total contribution of A = Rs. 24000 + Rs. 8000 = Rs. 32000
- Total contribution of B = Contribution for first 8 months + Contribution for last 4 months
- Total contribution of B = Rs. 32000 + Rs. 20000 = Rs. 52000

### Step 6: Find the ratio of contributions of A and B.
- The ratio of A's contribution to B's contribution = 32000 : 52000 = 32 : 52 = 8 : 13

### Step 7: Calculate A's share of the profit.
- Total profit = Rs. 630
- A's share = (A's ratio / Total ratio) * Total profit
- A's share = (8 / (8 + 13)) * 630 = (8 / 21) * 630

### Step 8: Calculate A's share.
- A's share = (8 / 21) * 630 = Rs. 240

### Final Answer:
A's share of the profit is Rs. 240.

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