The difference between the compound interest (compounded annually) and simple interest on a certain sum at 10 % per annum for 2 years is Rs 631 . Find the sum .

Options

A. Rs 80100
B. Rs 63100
C. Rs 60000
D. Rs 73100

Answer

To solve the problem step by step, we will use the formula for the difference between compound interest (CI) and simple interest (SI) for a period of 2 years.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Rate (r) = 10% per annum
- Time (t) = 2 years
- Difference (D) between CI and SI = Rs 631

2. **Use the Formula for the Difference:**
The formula for the difference between compound interest and simple interest for 2 years is:
\[ D = \frac{P \cdot r^2}{100^2} \]
where P is the principal amount.

3. **Substitute the Known Values into the Formula:**
Substitute D = 631 and r = 10 into the formula:
\[ 631 = \frac{P \cdot 10^2}{100^2} \]

4. **Calculate \(10^2\) and \(100^2\):**
- \(10^2 = 100\)
- \(100^2 = 10000\)

So the equation becomes:
\[ 631 = \frac{P \cdot 100}{10000} \]

5. **Simplify the Equation:**
Simplifying the right side gives:
\[ 631 = \frac{P}{100} \]

6. **Solve for P:**
To find P, multiply both sides by 100:
\[ P = 631 \times 100 \]
\[ P = 63100 \]

7. **Conclusion:**
The principal amount (sum) is Rs 63100.

### Final Answer:
The sum (principal) is Rs 63100.