The difference between the compound interest and simple interest on Rs x at 20% per annum for 2 years is Rs 147.5. What is the value of X?

Options

A. Rs 3,687.50
B. Rs 3,587.50
C. Rs 3,685.50
D. Rs 3,487.50

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 20% per annum for 2 years is Rs 147.5.

### Step 1: Formulate the Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (which is \( x \))
- \( R \) = Rate of interest (20%)
- \( T \) = Time (2 years)

Substituting the values:
\[ SI = \frac{x \times 20 \times 2}{100} = \frac{40x}{100} = 0.4x \]

### Step 2: Formulate the Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ CI = x \left(1 + \frac{20}{100}\right)^2 - x = x \left(1.2^2\right) - x \]
Calculating \( 1.2^2 \):
\[ 1.2^2 = 1.44 \]
So,
\[ CI = x \times 1.44 - x = 0.44x \]

### Step 3: Find the Difference Between CI and SI
Now, we can find the difference between CI and SI:
\[ CI - SI = 0.44x - 0.4x = 0.04x \]

### Step 4: Set Up the Equation
According to the problem, this difference is equal to Rs 147.5:
\[ 0.04x = 147.5 \]

### Step 5: Solve for \( x \)
To find \( x \), we divide both sides by 0.04:
\[ x = \frac{147.5}{0.04} = 3687.5 \]

### Final Answer
The value of \( x \) is Rs 3687.50.

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