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 using the information given about the amounts after 2 years and 3 years, we can follow these steps:

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

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

### Step 3: Calculate the total simple interest for 2 years
Now that we have the simple interest for 1 year, we can calculate the total simple interest for 2 years:
\[ SI_{2 \text{ years}} = SI \times 2 \]
\[ SI_{2 \text{ years}} = 650 \times 2 \]
\[ SI_{2 \text{ years}} = 1300 \]

### Step 4: Calculate the principal amount
The principal amount (P) can be calculated using the formula for the amount after 2 years:
\[ A2 = P + SI_{2 \text{ years}} \]
Rearranging the formula gives:
\[ P = A2 - SI_{2 \text{ years}} \]
Substituting the values:
\[ P = 5182 - 1300 \]
\[ P = 3882 \]

### Final Answer
The principal amount is Rs. 3,882.

---