Omdutt started a business with a capital of Rs 8000. After six months, Sanjay joined him with investment of some capital. If at the end of the year each of them gets equal amount as profit, how much did Sanjay invest in the business?

Options

A. Rs 18000
B. Rs 17500
C. Rs 16000
D. Rs 16500

Answer

To solve the problem, we need to determine how much Sanjay invested in the business so that both Omdutt and Sanjay receive equal profits at the end of the year.

### Step-by-Step Solution:

1. **Identify Omdutt's Investment and Duration:**
- Omdutt invested Rs. 8000.
- He invested this amount for 12 months (the entire year).

\[ \text{Omdutt's investment} = 8000 \text{ Rs for } 12 \text{ months} \]

2. **Calculate Omdutt's Capital Contribution in Terms of Months:**
- Omdutt's capital contribution in terms of capital-months is:

\[ \text{Omdutt's capital contribution} = 8000 \times 12 = 96000 \text{ Rs-months} \]

3. **Identify Sanjay's Investment and Duration:**
- Sanjay joined after 6 months, so he invested for 6 months.
- Let Sanjay's investment be \( x \) Rs.

\[ \text{Sanjay's investment} = x \text{ Rs for } 6 \text{ months} \]

4. **Calculate Sanjay's Capital Contribution in Terms of Months:**
- Sanjay's capital contribution in terms of capital-months is:

\[ \text{Sanjay's capital contribution} = x \times 6 \]

5. **Set Up the Equation for Equal Profit:**
- Since both received equal profit, their capital contributions in terms of capital-months must be equal:

\[ 96000 = x \times 6 \]

6. **Solve for \( x \):**
- Rearranging the equation gives:

\[ x = \frac{96000}{6} \]
\[ x = 16000 \]

7. **Conclusion:**
- Sanjay invested Rs. 16000 in the business.

### Final Answer:
Sanjay invested Rs. 16000.