Mr. X invested an amount for 2 years at 15 percent per annum at simple interest. Had the interest been compounded, he would have earned 450/- more as interest. What was the amount invested?

Options

A. 22000
B. 24000
C. 25000
D. None of these

Answer

To solve the problem step by step, we need to find the principal amount Mr. X invested based on the difference between simple interest and compound interest over 2 years.

### Step 1: Understand the given information
- The interest rate is 15% per annum.
- The investment period is 2 years.
- The difference between the compound interest and simple interest over this period is ₹450.

### Step 2: Use the formula for the difference between compound interest and simple interest
The formula for the difference between compound interest (CI) and simple interest (SI) after 2 years is:
\[ \text{Difference} = \frac{P \times r^2}{100^2} \]
Where:
- \( P \) = Principal amount
- \( r \) = Rate of interest

### Step 3: Substitute the known values into the formula
Given that the difference is ₹450 and the rate \( r \) is 15%, we can substitute these values into the formula:
\[ 450 = \frac{P \times 15^2}{100^2} \]

### Step 4: Simplify the equation
Calculating \( 15^2 \) and \( 100^2 \):
\[ 15^2 = 225 \quad \text{and} \quad 100^2 = 10000 \]
Now substituting these values into the equation:
\[ 450 = \frac{P \times 225}{10000} \]

### Step 5: Rearranging the equation to find \( P \)
To isolate \( P \), we can multiply both sides by 10000:
\[ 450 \times 10000 = P \times 225 \]
\[ 4500000 = P \times 225 \]

### Step 6: Solve for \( P \)
Now divide both sides by 225:
\[ P = \frac{4500000}{225} \]
Calculating this gives:
\[ P = 20000 \]

### Conclusion
The principal amount invested by Mr. X is ₹20,000.

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