The simple interest on a certain sum for 3 years at 10% per annum is Rs. 829.50. Find the sum.

Answer

To find the principal sum (P) given the simple interest (SI), rate (R), and time (T), we can use the formula for simple interest:

\[ SI = \frac{P \times R \times T}{100} \]

### Step-by-Step Solution:

1. **Identify the given values:**
- Simple Interest (SI) = Rs. 829.50
- Rate (R) = 10% per annum
- Time (T) = 3 years

2. **Substitute the known values into the formula:**
\[ 829.50 = \frac{P \times 10 \times 3}{100} \]

3. **Simplify the equation:**
- First, calculate \(10 \times 3 = 30\).
- The equation now looks like:
\[ 829.50 = \frac{P \times 30}{100} \]

4. **Multiply both sides by 100 to eliminate the fraction:**
\[ 829.50 \times 100 = P \times 30 \]
\[ 82950 = P \times 30 \]

5. **Now, divide both sides by 30 to solve for P:**
\[ P = \frac{82950}{30} \]

6. **Calculate the value of P:**
\[ P = 2765 \]

7. **Conclusion:**
The principal sum (P) is Rs. 2765.