In how many years will a sum of money become sixteen times itself at 30% p.a. simple interest?

Options

A. 25
B. 30
C. 50
D. 40

Answer

To solve the problem of how many years it will take for a sum of money to become sixteen times itself at a simple interest rate of 30% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the time (T) it takes for a principal amount (P) to grow to 16 times itself with a simple interest rate of 30% per annum.

2. **Define the Variables**:
- Let the principal amount (P) be \( x \).
- The amount after time \( T \) will be \( 16x \) (since it becomes 16 times itself).

3. **Calculate Simple Interest**:
- The formula for Simple Interest (SI) is:
\[ SI = \text{Amount} - \text{Principal} \]
- Therefore, the Simple Interest earned will be:
\[ SI = 16x - x = 15x \]

4. **Use the Simple Interest Formula**:
- The formula for Simple Interest is also given by:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, \( P = x \), \( R = 30\% \), and \( T \) is what we need to find. So we can set up the equation:
\[ 15x = \frac{x \times 30 \times T}{100} \]

5. **Simplify the Equation**:
- Cancel \( x \) from both sides (assuming \( x \neq 0 \)):
\[ 15 = \frac{30T}{100} \]
- This simplifies to:
\[ 15 = \frac{3T}{10} \]

6. **Solve for T**:
- Multiply both sides by 10:
\[ 150 = 3T \]
- Now divide both sides by 3:
\[ T = 50 \]

### Final Answer:
The time required for the sum of money to become sixteen times itself at 30% per annum simple interest is **50 years**.