The difference between the compound interest and simple interest on Rs x at 8% per annum for 2 years is Rs 19.20. What is the value of x?

Options

A. 2500
B. 3200
C. 2800
D. 3000

Answer

To find the value of \( x \) (the principal amount) given that the difference between the compound interest (CI) and simple interest (SI) for 2 years at an interest rate of 8% per annum is Rs 19.20, we can follow these steps:

### Step-by-Step Solution:

1. **Understand 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, and \( r \) is the rate of interest.

2. **Substitute the Known Values**:
We know that the difference is Rs 19.20, the rate \( r \) is 8%, and we need to find \( P \) (which is \( x \)):
\[ 19.20 = \frac{x \times 8^2}{100^2} \]

3. **Calculate \( 8^2 \) and \( 100^2 \)**:
\[ 8^2 = 64 \quad \text{and} \quad 100^2 = 10000 \]
So, we can rewrite the equation as:
\[ 19.20 = \frac{x \times 64}{10000} \]

4. **Multiply Both Sides by 10000**:
\[ 19.20 \times 10000 = x \times 64 \]
\[ 192000 = x \times 64 \]

5. **Divide Both Sides by 64**:
\[ x = \frac{192000}{64} \]

6. **Calculate the Value of \( x \)**:
\[ x = 3000 \]

Thus, the value of \( x \) (the principal amount) is Rs 3000.

### Final Answer:
The value of \( x \) is Rs 3000.

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