What sum lent at 10% per year on S.I. will amount to Rs. 450 in 2 years?

Options

A. Rs. 375
B. Rs. 240
C. Rs. 350
D. Rs.280

Answer

To solve the problem of finding the principal sum lent at 10% per year on Simple Interest that will amount to Rs. 450 in 2 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Total Amount (A) = Rs. 450
- Rate of Interest (R) = 10% per annum
- Time (T) = 2 years

2. **Recall the Formula for Total Amount in Simple Interest:**
The formula for the total amount (A) in Simple Interest is given by:
\[ A = P + SI \]
where \( SI \) (Simple Interest) can be calculated using:
\[ SI = \frac{P \times R \times T}{100} \]
Thus, we can rewrite the total amount formula as:
\[ A = P + \frac{P \times R \times T}{100} \]

3. **Substitute the Known Values into the Formula:**
Substitute \( A = 450 \), \( R = 10 \), and \( T = 2 \) into the equation:
\[ 450 = P + \frac{P \times 10 \times 2}{100} \]

4. **Simplify the Equation:**
Simplifying the interest term:
\[ \frac{10 \times 2}{100} = \frac{20}{100} = 0.2 \]
Therefore, the equation becomes:
\[ 450 = P + 0.2P \]
This can be combined as:
\[ 450 = 1.2P \]

5. **Solve for Principal (P):**
To find \( P \), divide both sides by 1.2:
\[ P = \frac{450}{1.2} \]

6. **Calculate the Value:**
Performing the division:
\[ P = 375 \]

### Conclusion:
The sum lent at 10% per year on Simple Interest that will amount to Rs. 450 in 2 years is **Rs. 375**.