In how many years will a sum be four times of itself at 15% rate of simple interest per annum?

Options

A. 10yr
B. 15yr
C. 20yr
D. 30yr

Answer

To solve the problem of how many years it will take for a sum to become four times itself at a simple interest rate of 15% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Principal Amount**:
Let the principal amount be \( P = x \).

2. **Determine the Final Amount**:
Since we want the amount to be four times the principal, the final amount \( A \) will be:
\[ A = 4x \]

3. **Calculate the Simple Interest**:
The simple interest \( SI \) can be calculated using the formula:
\[ SI = A - P \]
Substituting the values we have:
\[ SI = 4x - x = 3x \]

4. **Use the Simple Interest Formula**:
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest per annum,
- \( T \) is the time in years.

Substituting the known values into the formula:
\[ 3x = \frac{x \times 15 \times T}{100} \]

5. **Cancel the Principal**:
Since \( x \) is common on both sides, we can cancel it (assuming \( x \neq 0 \)):
\[ 3 = \frac{15T}{100} \]

6. **Solve for Time \( T \)**:
Rearranging the equation to solve for \( T \):
\[ 3 \times 100 = 15T \]
\[ 300 = 15T \]
\[ T = \frac{300}{15} = 20 \]

7. **Conclusion**:
Therefore, it will take **20 years** for the sum to become four times itself at a simple interest rate of 15% per annum.

### Final Answer:
The answer is **20 years**.