The difference between the compound interest and simple interst on Rs. X at `8.5%` per annum for 2 years is Rs. 65.025. What is the value of x ?

Options

A. 8625
B. 8500
C. 9000
D. 8750

Answer

To solve the problem, we will use the formula that relates the difference between compound interest (CI) and simple interest (SI) when the time period is 2 years.

### Step-by-Step Solution:

1. **Identify the given values**:
- Rate (R) = 8.5%
- Time (T) = 2 years
- Difference between CI and SI = Rs. 65.025

2. **Use the formula for the difference between CI and SI**:
The formula for the difference between compound interest and simple interest for 2 years is given by:
\[ \text{Difference} = \frac{P \times R^2}{100^2} \]
where \( P \) is the principal amount (Rs. X) and \( R \) is the rate of interest.

3. **Substitute the known values into the formula**:
\[ 65.025 = \frac{X \times (8.5)^2}{100^2} \]

4. **Calculate \( (8.5)^2 \)**:
\[ (8.5)^2 = 72.25 \]

5. **Substitute \( (8.5)^2 \) back into the equation**:
\[ 65.025 = \frac{X \times 72.25}{10000} \]

6. **Multiply both sides by 10000 to eliminate the fraction**:
\[ 650250 = X \times 72.25 \]

7. **Solve for \( X \)**:
\[ X = \frac{650250}{72.25} \]

8. **Calculate \( X \)**:
\[ X = 9000 \]

Thus, the value of \( X \) is Rs. 9000.