In a special plan, a sum invested at rate of simple interest becomes triple in 8 years. How long will it take to make it 4 times?

Options

A. 11 years 6 months
B. 10 years 8 months
C. 10 years
D. 12 years

Answer

To solve the problem step by step, we will use the concept of simple interest.

### Step-by-Step Solution:

1. **Understanding the Problem:**
We know that a certain principal amount (let's denote it as \( P \)) becomes triple in 8 years under simple interest. We need to find out how long it will take for the same principal to become four times.

2. **Let’s Define the Principal:**
Let the principal amount be \( P = X \).

3. **Calculate the Amount When It Becomes Triple:**
If the principal becomes triple, then the amount \( A \) after 8 years is:
\[ A = 3P = 3X \]

4. **Calculate the Simple Interest:**
The simple interest \( SI \) earned in 8 years is:
\[ SI = A - P = 3X - X = 2X \]

5. **Using the Simple Interest Formula:**
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Here, \( T = 8 \) years, and we can denote the rate of interest as \( R \). Thus, we can write:
\[ 2X = \frac{X \times R \times 8}{100} \]

6. **Simplifying the Equation:**
Dividing both sides by \( X \) (assuming \( X \neq 0 \)):
\[ 2 = \frac{R \times 8}{100} \]
Rearranging gives:
\[ R = \frac{2 \times 100}{8} = 25\% \]

7. **Calculating the Time to Make It Four Times:**
Now, we need to find out how long it will take for the principal to become four times:
\[ A = 4P = 4X \]
The simple interest in this case will be:
\[ SI = A - P = 4X - X = 3X \]

8. **Using the Simple Interest Formula Again:**
Using the same formula for simple interest:
\[ 3X = \frac{X \times R \times T}{100} \]
Substituting \( R = 25 \):
\[ 3X = \frac{X \times 25 \times T}{100} \]

9. **Simplifying the Equation:**
Dividing both sides by \( X \):
\[ 3 = \frac{25T}{100} \]
Rearranging gives:
\[ 25T = 300 \]
Thus:
\[ T = \frac{300}{25} = 12 \text{ years} \]

### Final Answer:
It will take **12 years** for the investment to become four times.

---