The difference between simple interest and compound interest on a certain sum of money for three years at `10%` per annum is Rs. 15 and 50 paise. The sum is:

Options

A. Rs. 5,000
B. Rs. 550
C. Rs. 5,500
D. Rs.500

Answer

To solve the problem, we need to find the principal amount based on the difference between simple interest (SI) and compound interest (CI) for 3 years at a rate of 10% per annum, which is given as Rs. 15.50.

### Step-by-Step Solution:

1. **Understanding the Difference Between SI and CI**:
The difference between the simple interest and compound interest for 3 years can be calculated using the formula:
\[ \text{Difference} = \text{CI} - \text{SI} = \frac{P \cdot r^2}{100^2} \]
where \( P \) is the principal amount and \( r \) is the rate of interest.

2. **Substituting the Values**:
Here, the rate \( r = 10\% \) and the difference is given as Rs. 15.50. We can substitute these values into the formula:
\[ 15.50 = \frac{P \cdot (10)^2}{100^2} \]

3. **Simplifying the Equation**:
This simplifies to:
\[ 15.50 = \frac{P \cdot 100}{10000} \]
\[ 15.50 = \frac{P}{100} \]

4. **Finding the Principal Amount**:
To find \( P \), we multiply both sides of the equation by 100:
\[ P = 15.50 \times 100 \]
\[ P = 1550 \]

5. **Conclusion**:
Therefore, the principal amount is Rs. 1550.

### Final Answer:
The sum is Rs. 1550.