The difference between the compound interest and simple interest on Rs. X at 11% per annum for 2 years is Rs. 60.50. What is the value of x ?

Options

A. 4800
B. 4000
C. 5000
D. 4500

Answer

To solve the problem, we need to find the value of \( X \) given that the difference between the compound interest (CI) and simple interest (SI) on \( X \) at an interest rate of 11% per annum for 2 years is Rs. 60.50.

### Step-by-Step Solution:

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

2. **Substituting Values**: Here, the difference is given as Rs. 60.50, and the rate \( r \) is 11%. We can substitute these values into the formula:
\[ 60.50 = \frac{X \cdot (11)^2}{100^2} \]

3. **Calculating \( r^2 \)**: Calculate \( 11^2 \):
\[ 11^2 = 121 \]
Therefore, the equation becomes:
\[ 60.50 = \frac{X \cdot 121}{10000} \]

4. **Rearranging the Equation**: Multiply both sides by 10000 to eliminate the fraction:
\[ 60.50 \cdot 10000 = X \cdot 121 \]
Simplifying this gives:
\[ 605000 = X \cdot 121 \]

5. **Solving for \( X \)**: Now, divide both sides by 121 to find \( X \):
\[ X = \frac{605000}{121} \]

6. **Calculating \( X \)**: Perform the division:
\[ X = 5000 \]

### Final Answer:
The value of \( X \) is Rs. 5000.