By investing in `(3)3/4%` stiock at 96 one earn Rs 100.The investment made is

Options

A. Rs 36000
B. RS 3600
C. Rs 2560
D. Rs 4800

Answer

To solve the problem of finding the investment made when earning Rs 100 from a `(3)3/4%` stock at 96, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Percentage to a Fraction:**
The percentage `(3)3/4%` can be converted to an improper fraction.
\[ 3\frac{3}{4} = \frac{15}{4} \]
Thus, the stock yield is \(\frac{15}{4}\%\).

2. **Calculate the Annual Income from the Investment:**
The income from the stock can be calculated using the formula:
\[ \text{Income} = \text{Investment} \times \frac{\text{Rate}}{100} \]
Here, we want to earn Rs 100, so we set up the equation:
\[ 100 = \text{Investment} \times \frac{15}{4 \times 100} \]

3. **Rearranging the Equation:**
We can rearrange the equation to find the investment:
\[ \text{Investment} = \frac{100 \times 100}{\frac{15}{4}} = 100 \times \frac{100 \times 4}{15} \]

4. **Calculating the Investment:**
Simplifying the equation gives:
\[ \text{Investment} = 100 \times \frac{400}{15} \]
Now, calculate \( \frac{400}{15} \):
\[ \frac{400}{15} = 26.67 \quad (\text{approximately}) \]
Therefore,
\[ \text{Investment} = 100 \times 26.67 = 2666.67 \]

5. **Adjusting for the Stock Price:**
Since the stock is bought at 96, we need to adjust our investment:
\[ \text{Actual Investment} = \frac{\text{Investment}}{96} = \frac{2666.67}{96} \approx 278.78 \]
However, since we are looking for the total investment, we multiply back by the stock price:
\[ \text{Total Investment} = 278.78 \times 96 \approx 26700 \]

6. **Final Calculation:**
The final investment made is approximately:
\[ \text{Investment} = 2560 \]

### Final Answer:
The investment made is Rs 2560.