A sum fetched a total simple interest of Rs. 7728 at the rate of 7 % per annum in 8 years . What is the sum ?

Options

A. Rs. 13800
B. Rs. 16560
C. Rs. 11040
D. Rs. 8280

Answer

To solve the problem of finding the principal amount that fetched a total simple interest of Rs. 7728 at the rate of 7% per annum over 8 years, we can follow these steps:

### Step-by-Step Solution:

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

2. **Substitute the Known Values**:
From the problem, we know:
- \( SI = 7728 \)
- \( R = 7\% \)
- \( T = 8 \) years

Plugging these values into the formula gives us:
\[ 7728 = \frac{P \times 7 \times 8}{100} \]

3. **Simplify the Equation**:
First, calculate \( 7 \times 8 \):
\[ 7 \times 8 = 56 \]
So the equation becomes:
\[ 7728 = \frac{P \times 56}{100} \]

4. **Multiply Both Sides by 100**:
To eliminate the fraction, multiply both sides by 100:
\[ 7728 \times 100 = P \times 56 \]
This simplifies to:
\[ 772800 = P \times 56 \]

5. **Solve for Principal (P)**:
Now, divide both sides by 56 to find \( P \):
\[ P = \frac{772800}{56} \]

6. **Calculate the Division**:
Performing the division:
\[ P = 13800 \]

7. **Conclusion**:
Therefore, the principal amount is:
\[ P = Rs. 13800 \]

### Final Answer:
The sum (principal) is Rs. 13800.