The difference between C.I & S.I on a certain sum at 10 % per annum for 2 years is Rs. 631. Find the sum

Answer

To solve the problem of finding the sum (principal) given the difference between compound interest (C.I) and simple interest (S.I) for 2 years at a rate of 10% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**:
The difference between Compound Interest (C.I) and Simple Interest (S.I) for 2 years can be calculated using the formula:
\[ C.I - S.I = \frac{P \cdot r^2}{100^2} \]
where:
- \( P \) = principal (the sum we need to find)
- \( r \) = rate of interest (10% in this case)

2. **Substitute the Known Values**:
We know that the difference \( C.I - S.I = 631 \) and \( r = 10 \). Therefore, we can substitute these values into the formula:
\[ 631 = \frac{P \cdot (10)^2}{100^2} \]

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

Now, substitute these values back into the equation:
\[ 631 = \frac{P \cdot 100}{10000} \]

4. **Simplify the Equation**:
We can simplify the equation:
\[ 631 = \frac{P}{100} \quad \text{(since } \frac{100}{10000} = \frac{1}{100}\text{)} \]

5. **Solve for \( P \)**:
To find \( P \), multiply both sides of the equation by 100:
\[ P = 631 \times 100 \]
\[ P = 63100 \]

### Final Answer:
The principal (sum) is Rs. 63,100.

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