The difference between the compound interest and simple interest on a certain sum for 2 years at 10% per annum is Rs300. Find the sum.
किसी राशि पर चक्रवृद्धि ब्याज और साधारण ब्याज के बीच 10% प्रतिवर्ष पर 2 वर्ष के लिए अंतर Rs 300 है। राशि ज्ञात करें।

Options

A. Rs 30,000
B. Rs 30,500
C. Rs 31,000
D. Rs 31,500

Explanation

To solve the problem, we need to find the principal amount (sum) based on the given information about the difference between compound interest (CI) and simple interest (SI) over 2 years at a rate of 10% per annum.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Rate of interest (r) = 10% per annum
- Time (t) = 2 years
- Difference between CI and SI = Rs 300

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

3. **Substitute the Known Values:**
We know the difference is Rs 300, the rate \( r = 10 \), and time \( t = 2 \). Plugging these values into the formula gives:
\[ 300 = \frac{P \cdot 10^2}{100^2} \]

4. **Simplify the Equation:**
\[ 300 = \frac{P \cdot 100}{10000} \]
\[ 300 = \frac{P}{100} \]

5. **Solve for the Principal Amount (P):**
To find \( P \), multiply both sides by 100:
\[ P = 300 \cdot 100 \]
\[ P = 30000 \]

6. **Conclusion:**
The principal amount is Rs 30,000.