The difference between compound interest and simple interest on Rs x at 8% per annum for 2 years is Rs 48. What is the value of x ?

Options

A. 80
B. 7500
C. 74
D. 7800

Answer

To find the value of \( x \) given that the difference between compound interest (CI) and simple interest (SI) on \( Rs. x \) at 8% per annum for 2 years is \( Rs. 48 \), we can follow these steps:

### Step 1: Understand the formula for the difference between CI and SI
The difference between 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, \( R \) is the rate of interest, and the time period is 2 years.

### Step 2: Substitute the known values into the formula
Here, we know:
- Difference = \( Rs. 48 \)
- Rate \( R = 8\% \)

Substituting these values into the formula gives:
\[ 48 = \frac{x \cdot 8^2}{100^2} \]

### Step 3: Simplify the equation
Calculating \( 8^2 \):
\[ 8^2 = 64 \]
Now substituting this back into the equation:
\[ 48 = \frac{x \cdot 64}{10000} \]

### Step 4: Rearranging the equation to solve for \( x \)
To isolate \( x \), multiply both sides by \( 10000 \):
\[ 48 \cdot 10000 = 64x \]
\[ 480000 = 64x \]

### Step 5: Solve for \( x \)
Now, divide both sides by 64:
\[ x = \frac{480000}{64} \]
Calculating this gives:
\[ x = 7500 \]

### Final Answer
Thus, the value of \( x \) is \( Rs. 7500 \).

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