A starts a business with 6000 and B joins the business 4 months later with an investment of Rs. 8000. After one year, they earn a profit of Rs. 34000. Find the share of A in profit.

Options

A. Rs. 18000
B. Rs. 16000
C. Rs. 19000
D. Rs. 15000

Answer

To find the share of A in the profit, we first need to calculate the effective capital contribution of both A and B over the time they were invested in the business.

### Step-by-Step Solution:

1. **Calculate A's Investment Contribution**:
- A invests Rs. 6000 for the entire year (12 months).
- Therefore, A's contribution in terms of capital months = Investment × Time = 6000 × 12 = 72000.

2. **Calculate B's Investment Contribution**:
- B joins the business 4 months later, meaning he invests for 8 months.
- B invests Rs. 8000.
- Therefore, B's contribution in terms of capital months = Investment × Time = 8000 × 8 = 64000.

3. **Total Contribution**:
- Total contribution = A's contribution + B's contribution = 72000 + 64000 = 136000.

4. **Calculate the Profit Sharing Ratio**:
- A's share of the profit is based on his contribution to the total capital.
- The ratio of A's contribution to the total contribution = 72000 : 136000.
- Simplifying this ratio:
- Divide both sides by 8000:
- A's share = 72000 / 8000 = 9
- Total share = 136000 / 8000 = 17
- Thus, the ratio of A's to B's share = 9 : 17.

5. **Calculate A's Share of the Profit**:
- Total profit earned = Rs. 34000.
- A's share of the profit = (A's ratio / Total ratio) × Total profit = (9 / 26) × 34000.
- A's share = (9 × 34000) / 26 = 306000 / 26 = 11700.

### Final Answer:
A's share in the profit is Rs. 11700.

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