Sunetra started a business of software with Rs. 50,000. After 6 months Nikhil joined her with Rs. 80,000. At the end of 3 years they earned a profit of Rs. 24,500. What is the share of Sunetra in the profit?

Options

A. Rs. 14,000
B. Rs. 9,423
C. Rs. 10,250
D. None of these

Answer

To find the share of Sunetra in the profit, we need to calculate the effective capital contribution of both Sunetra and Nikhil over the time they invested in the business.

### Step 1: Calculate the time of investment for each partner.
- Sunetra invested Rs. 50,000 for the entire 3 years (36 months).
- Nikhil joined after 6 months, so he invested Rs. 80,000 for 2.5 years (30 months).

### Step 2: Calculate the capital contribution for each partner.
- For Sunetra:
\[ \text{Capital Contribution of Sunetra} = \text{Investment} \times \text{Time} = 50,000 \times 36 = 1,800,000 \]

- For Nikhil:
\[ \text{Capital Contribution of Nikhil} = \text{Investment} \times \text{Time} = 80,000 \times 30 = 2,400,000 \]

### Step 3: Calculate the total capital contribution.
\[ \text{Total Capital Contribution} = \text{Capital Contribution of Sunetra} + \text{Capital Contribution of Nikhil} = 1,800,000 + 2,400,000 = 4,200,000 \]

### Step 4: Determine the share of each partner in the total capital contribution.
- Share of Sunetra:
\[ \text{Share of Sunetra} = \frac{\text{Capital Contribution of Sunetra}}{\text{Total Capital Contribution}} = \frac{1,800,000}{4,200,000} = \frac{18}{42} = \frac{3}{7} \]

- Share of Nikhil:
\[ \text{Share of Nikhil} = \frac{\text{Capital Contribution of Nikhil}}{\text{Total Capital Contribution}} = \frac{2,400,000}{4,200,000} = \frac{24}{42} = \frac{4}{7} \]

### Step 5: Calculate Sunetra's share of the profit.
- Total Profit = Rs. 24,500
- Sunetra's Share of Profit:
\[ \text{Sunetra's Share of Profit} = \text{Total Profit} \times \text{Share of Sunetra} = 24,500 \times \frac{3}{7} = 10,500 \]

### Final Answer:
Sunetra's share in the profit is Rs. 10,500.

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