In simple interest rate per annum a certain sum amounts to Rs. 5,182 in 2 years and Rs. 5,832 in 3 years. The principal in rupees is

Options

A. Rs. 2882
B. Rs. 5000
C. Rs. 3882
D. Rs. 4000

Answer

To find the principal amount based on the information given about the simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the amounts for 2 and 3 years**:
- Amount after 2 years (A2) = Rs. 5,182
- Amount after 3 years (A3) = Rs. 5,832

2. **Calculate the simple interest for 1 year**:
- The simple interest for 1 year (SI) can be found by subtracting the amount after 2 years from the amount after 3 years:
\[ SI = A3 - A2 = 5832 - 5182 = 650 \]

3. **Calculate the total simple interest for 2 years**:
- Since the interest is the same each year, the total simple interest for 2 years (SI for 2 years) will be:
\[ SI_{2\text{ years}} = 2 \times SI = 2 \times 650 = 1300 \]

4. **Determine the principal amount**:
- The principal (P) can be calculated by subtracting the total simple interest for 2 years from the amount after 2 years:
\[ P = A2 - SI_{2\text{ years}} = 5182 - 1300 = 3882 \]

5. **Final answer**:
- The principal amount is Rs. 3,882.