Karan started a business investing Rs 29000. After five months, Satish joined with a capital of Rs 18000. If at the end of the year, they earn a profit of Rs. 16970, then what will be the share of Satish in the profit ?

Options

A. A) Rs. 5422
B. B) Rs. 5489
C. C) Rs. 4511
D. D) Rs. 6145

Answer

To find Satish's share of the profit, we need to calculate the effective capital contribution of both Karan and Satish over the time they invested in the business.

### Step-by-Step Solution:

1. **Identify the Investments and Time Periods:**
- Karan's investment: Rs 29,000 for 12 months.
- Satish's investment: Rs 18,000 for 7 months (since he joined after 5 months).

2. **Calculate the Capital Contribution:**
- Karan's contribution:
\[ \text{Karan's Contribution} = 29000 \times 12 = 348000 \]
- Satish's contribution:
\[ \text{Satish's Contribution} = 18000 \times 7 = 126000 \]

3. **Calculate the Total Capital Contribution:**
- Total contribution:
\[ \text{Total Contribution} = 348000 + 126000 = 474000 \]

4. **Determine the Ratio of Contributions:**
- The ratio of Karan's to Satish's contributions:
\[ \text{Ratio} = \frac{348000}{126000} = \frac{348}{126} = \frac{58}{21} \]

5. **Calculate Satish's Share of the Profit:**
- Total profit earned: Rs 16,970.
- Satish's share of the profit:
\[ \text{Satish's Share} = \frac{21}{58 + 21} \times 16970 = \frac{21}{79} \times 16970 \]

6. **Perform the Calculation:**
- Calculate Satish's share:
\[ \text{Satish's Share} = \frac{21 \times 16970}{79} = \frac{356370}{79} \approx 4515.84 \]

7. **Final Answer:**
- Satish's share in the profit is approximately Rs 4515.84.