A sum fetched a total simple interest of ₹ 1,350 at 9% p.a. in 5 years. What is the sum?

Options

A. ₹2,000
B. ₹3,300
C. ₹2,500
D. ₹3,000

Answer

To find the principal sum (P) that fetched a total simple interest of ₹1,350 at a rate of 9% per annum over 5 years, we can use the formula for simple interest (SI):

### Step-by-Step Solution:

1. **Understand the formula for Simple Interest (SI)**:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the sum we want to find)
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

2. **Substitute the known values into the formula**:
We know:
- \( SI = 1350 \)
- \( R = 9\% \)
- \( T = 5 \) years

Plugging these values into the formula gives:
\[ 1350 = \frac{P \times 9 \times 5}{100} \]

3. **Simplify the equation**:
First, calculate \( 9 \times 5 = 45 \):
\[ 1350 = \frac{P \times 45}{100} \]

4. **Multiply both sides by 100 to eliminate the fraction**:
\[ 1350 \times 100 = P \times 45 \]
\[ 135000 = P \times 45 \]

5. **Solve for P**:
Divide both sides by 45:
\[ P = \frac{135000}{45} \]

6. **Calculate the value**:
\[ P = 3000 \]

Thus, the principal sum is ₹3,000.

### Final Answer:
The sum (principal) is ₹3,000.