Jayant started a business investing Rs. 6000. Six months later Madhu joined him investing Rs. 4000. If they make a profit of Rs. 5200 at the end of the year, how much should be the share of Madhu?

Options

A. Rs. 1300
B. Rs. 1732
C. Rs. 3466
D. Rs. 3900

Answer

To solve the problem, we need to calculate the share of Madhu in the total profit based on their investments and the time for which they invested.

### Step-by-Step Solution:

1. **Calculate the investment time for each partner**:
- Jayant invested Rs. 6000 for the entire year (12 months).
- Madhu invested Rs. 4000 for 6 months (since he joined 6 months later).

2. **Calculate the effective capital contribution**:
- For Jayant:
\[ \text{Effective Capital} = \text{Investment} \times \text{Time} = 6000 \times 12 = 72000 \]
- For Madhu:
\[ \text{Effective Capital} = \text{Investment} \times \text{Time} = 4000 \times 6 = 24000 \]

3. **Calculate the total effective capital**:
\[ \text{Total Effective Capital} = \text{Jayant's Effective Capital} + \text{Madhu's Effective Capital} = 72000 + 24000 = 96000 \]

4. **Determine the profit-sharing ratio**:
- Jayant's share of the profit:
\[ \text{Jayant's Share} = \frac{72000}{96000} = \frac{3}{4} \]
- Madhu's share of the profit:
\[ \text{Madhu's Share} = \frac{24000}{96000} = \frac{1}{4} \]

5. **Calculate Madhu's share of the total profit**:
- Total profit = Rs. 5200
- Madhu's share of the profit:
\[ \text{Madhu's Share of Profit} = \text{Total Profit} \times \text{Madhu's Share Ratio} = 5200 \times \frac{1}{4} = 1300 \]

### Conclusion:
Madhu's share of the profit is **Rs. 1300**.

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