A sum was doubled with `12(1/2)%` rate of simple interest, per annum. Then time taken for that sum is

Options

A. 10 years
B. 8 years
C. `12 1/2` years
D. `8 1/2` years

Answer

To solve the problem of how long it takes for a sum to double at a simple interest rate of \(12.5\%\) per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
We need to find the time taken for a sum of money (let's call it \(X\)) to double at a simple interest rate of \(12.5\%\).

2. **Define the Variables**:
- Let the principal amount (initial sum) be \(X\).
- The amount after doubling will be \(2X\).
- The rate of interest is \(12.5\%\) per annum.

3. **Calculate Simple Interest**:
The simple interest (SI) earned when the sum doubles can be calculated as:
\[ \text{SI} = \text{Amount} - \text{Principal} = 2X - X = X \]

4. **Use the Simple Interest Formula**:
The formula for simple interest is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \(P\) is the principal amount (which is \(X\)),
- \(R\) is the rate of interest (which is \(12.5\%\)),
- \(T\) is the time in years (which we need to find).

5. **Substituting Values into the Formula**:
Substitute the values into the simple interest formula:
\[ X = \frac{X \times 12.5 \times T}{100} \]

6. **Cancel Out \(X\)**:
Since \(X\) is common on both sides, we can cancel it out (assuming \(X \neq 0\)):
\[ 1 = \frac{12.5 \times T}{100} \]

7. **Rearranging the Equation**:
Rearranging gives us:
\[ 12.5 \times T = 100 \]

8. **Solving for \(T\)**:
To find \(T\), divide both sides by \(12.5\):
\[ T = \frac{100}{12.5} \]

9. **Calculating \(T\)**:
Simplifying the division:
\[ T = 8 \]

### Conclusion:
The time taken for the sum to double at a simple interest rate of \(12.5\%\) per annum is **8 years**.