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

Options

A. A) 24000
B. B) 16000
C. C) 12000
D. D) 32000

Answer

To solve the problem step by step, we will use the concept of capital investment and profit sharing based on the time for which the capital was invested.

### Step-by-Step Solution:

1. **Identify the Initial Investment and Time Period:**
- Dileep's initial investment: Rs. 8000
- Time period for Dileep's investment: 12 months (1 year)
- Narender joins after 6 months, so his investment time period: 6 months.

2. **Let Narender's Investment be x:**
- We will denote Narender's investment as Rs. x.

3. **Calculate the Effective Investment:**
- Dileep's effective investment can be calculated as:
\[ \text{Dileep's effective investment} = 8000 \times 12 = 96000 \]
- Narender's effective investment can be calculated as:
\[ \text{Narender's effective investment} = x \times 6 = 6x \]

4. **Set Up the Equation Based on Profit Sharing:**
- Since both receive equal profit at the end of the year, we can set up the equation:
\[ \text{Dileep's effective investment} = \text{Narender's effective investment} \]
\[ 96000 = 6x \]

5. **Solve for x:**
- To find x, divide both sides of the equation by 6:
\[ x = \frac{96000}{6} = 16000 \]

6. **Conclusion:**
- Narender invested Rs. 16000 in the business.

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