The difference between the compound interest and the simple interest on a certain sum at `5%` per annum for 2 years is Rs. 1.50.The sum is—

Options

A. Rs. 600
B. Rs. 500
C. Rs.400
D. Rs.300

Answer

To find the sum (principal) based on the given information about the difference between compound interest (CI) and simple interest (SI), we can follow these steps:

### Step 1: Understand the relationship between CI and SI
The difference between compound interest and simple interest for 2 years can be expressed with the formula:
\[ \text{Difference} = \text{CI} - \text{SI} = \frac{P \times r^2}{100^2} \]
Where:
- \( P \) = Principal amount (the sum we want to find)
- \( r \) = Rate of interest (5% in this case)

### Step 2: Substitute the known values into the formula
Given that the difference is Rs. 1.50 and the rate \( r = 5\% \):
\[ 1.50 = \frac{P \times (5)^2}{100^2} \]

### Step 3: Simplify the equation
Calculating \( (5)^2 \) gives us 25 and \( 100^2 \) gives us 10000:
\[ 1.50 = \frac{P \times 25}{10000} \]

### Step 4: Rearrange the equation to solve for \( P \)
Multiply both sides by 10000 to eliminate the fraction:
\[ 1.50 \times 10000 = P \times 25 \]
\[ 15000 = P \times 25 \]

### Step 5: Divide both sides by 25
To isolate \( P \):
\[ P = \frac{15000}{25} \]

### Step 6: Calculate the value of \( P \)
\[ P = 600 \]

### Conclusion
The sum (principal) is Rs. 600.

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