On what sum of money will the SI for 7 yr 6 onths at 5% per annum be Rs 450 ?

Options

A. Rs 11000
B. Rs 1200
C. Rs 13000
D. Rs 12000

Answer

To find the principal amount (P) on which the simple interest (SI) for 7 years and 6 months at a rate of 5% per annum is Rs 450, we can use the formula for simple interest:

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

Where:
- SI = Simple Interest
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years

### Step-by-Step Solution:

1. **Convert the Time Period**:
The time given is 7 years and 6 months. We need to convert this into years.
\[ T = 7 + \frac{6}{12} = 7 + 0.5 = 7.5 \text{ years} \]

2. **Substitute the Values into the SI Formula**:
We know that SI = Rs 450, R = 5%, and T = 7.5 years. Substitute these values into the formula:
\[ 450 = \frac{P \times 5 \times 7.5}{100} \]

3. **Simplify the Equation**:
To eliminate the fraction, multiply both sides by 100:
\[ 450 \times 100 = P \times 5 \times 7.5 \]
\[ 45000 = P \times 37.5 \]

4. **Solve for P**:
Now, divide both sides by 37.5 to find P:
\[ P = \frac{45000}{37.5} \]
\[ P = 1200 \]

Thus, the principal amount is Rs 1200.

### Final Answer:
The sum of money on which the SI for 7 years and 6 months at 5% per annum will be Rs 450 is **Rs 1200**.