A starts a business with Rs6000 and B joins the business 4 moths 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. Rs16000
C. Rs 19000
D. Rs15000

Explanation

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

### Step 1: Calculate the investment duration for A and B
- A invests Rs. 6000 for 12 months.
- B invests Rs. 8000 but joins 4 months later, so B invests for 8 months.

### Step 2: Calculate the capital contribution of A and B
- A's contribution in terms of capital-months = Investment × Time = 6000 × 12 = 72000 capital-months.
- B's contribution in terms of capital-months = Investment × Time = 8000 × 8 = 64000 capital-months.

### Step 3: Determine the total capital-months
- Total capital-months = A's contribution + B's contribution = 72000 + 64000 = 136000 capital-months.

### Step 4: Calculate the ratio of their contributions
- The ratio of A's contribution to B's contribution = A's contribution : B's contribution = 72000 : 64000.
- Simplifying the ratio:
- Divide both sides by 8000:
- A : B = 9 : 8.

### Step 5: Calculate the total profit share
- Total profit = Rs. 34000.
- Total parts in the ratio = 9 + 8 = 17 parts.

### Step 6: Calculate A's share of the profit
- A's share of the profit = (A's ratio / Total ratio) × Total profit
- A's share = (9 / 17) × 34000 = 18000.

### Conclusion
- A's share in the profit is Rs. 18000.

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