By investing in a `6%` stock at 96 an income of Rs. 100 is obtained by making an investment of

Options

A. Rs 1600
B. Rs 1504
C. Rs 1666.66
D. RS 5760

Answer

To solve the problem, we need to determine the amount of investment required to obtain an income of Rs. 100 from a 6% stock that is priced at 96.

### Step-by-Step Solution:

1. **Understand the Stock and Income Relationship**:
- A 6% stock means that for every Rs. 100 of nominal value, the income (dividend) is Rs. 6.
- The stock is being purchased at Rs. 96, which means we are paying Rs. 96 to receive Rs. 6 in income.

2. **Calculate the Investment for Rs. 6 Income**:
- The investment required to earn Rs. 6 can be calculated as follows:
\[ \text{Investment for Rs. 6 income} = 96 \text{ (price of stock)} \]

3. **Calculate the Investment for Rs. 100 Income**:
- To find out how much investment is needed to earn Rs. 100, we can set up a proportion based on the income:
\[ \text{Investment} = \left( \frac{\text{Price of stock}}{\text{Income from stock}} \right) \times \text{Desired Income} \]
- Substituting the known values:
\[ \text{Investment} = \left( \frac{96}{6} \right) \times 100 \]

4. **Perform the Calculation**:
- First, calculate \( \frac{96}{6} \):
\[ \frac{96}{6} = 16 \]
- Now multiply by 100:
\[ 16 \times 100 = 1600 \]

5. **Conclusion**:
- The investment required to obtain an income of Rs. 100 is Rs. 1600.

### Final Answer:
The investment required is **Rs. 1600**.

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