Abhishek started a business investing '50,000. After one year he invested another '30,000 and Sudin also joined him with a capital of '70,000. If the profit earned in three years from the starting of business was '87,500, then find the share of Sudin in the profit.

Options

A. `'37,500`
B. `'35,000`
C. `'38,281`
D. `'52,500`

Answer

To find Sudin's share in the profit, we need to calculate the effective capital contribution of both Abhishek and Sudin over the 3 years.

### Step-by-Step Solution:

1. **Calculate Abhishek's Total Investment:**
- Abhishek initially invested ₹50,000 for 3 years.
- After 1 year, he invested an additional ₹30,000, which means this amount was invested for 2 years.
- Total investment by Abhishek:
- For the first ₹50,000:
\[ 50,000 \times 3 = 150,000 \]
- For the additional ₹30,000:
\[ 30,000 \times 2 = 60,000 \]
- Total contribution of Abhishek:
\[ 150,000 + 60,000 = 210,000 \]

2. **Calculate Sudin's Total Investment:**
- Sudin joined the business with ₹70,000, which was invested for 2 years.
- Total investment by Sudin:
\[ 70,000 \times 2 = 140,000 \]

3. **Calculate Total Investment:**
- Total investment from both partners:
\[ 210,000 + 140,000 = 350,000 \]

4. **Calculate the Profit Sharing Ratio:**
- The profit sharing ratio is based on the effective capital contributions:
- Abhishek's share:
\[ \text{Abhishek's share} = 210,000 \]
- Sudin's share:
\[ \text{Sudin's share} = 140,000 \]
- Therefore, the ratio of their investments is:
\[ \text{Ratio} = \frac{210,000}{140,000} = \frac{21}{14} = \frac{3}{2} \]

5. **Calculate Sudin's Share of the Profit:**
- Total profit earned is ₹87,500.
- Total parts in the ratio (3 + 2 = 5).
- Sudin's share in the profit:
\[ \text{Sudin's share} = \frac{2}{5} \times 87,500 = 35,000 \]

### Final Answer:
Sudin's share in the profit is ₹35,000.