A certain sum becomes 7 times in 8 years, at simple interest, then in how many years it will become 19 times?

Options

A. 15
B. 18
C. 28
D. 24

Answer

To solve the problem, we need to determine how many years it will take for a certain sum of money to become 19 times its original amount at simple interest, given that it becomes 7 times in 8 years.

### Step-by-Step Solution:

1. **Understand the Problem**: We know that a certain sum becomes 7 times in 8 years. This means if the principal amount (P) is 100, the amount (A) after 8 years is 700.

2. **Calculate Simple Interest**:
- The simple interest (SI) earned in 8 years can be calculated as:
\[ SI = A - P = 700 - 100 = 600 \]

3. **Determine the Rate of Interest**:
- The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, P = 100, SI = 600, and T = 8 years. We need to find the rate (R):
\[ 600 = \frac{100 \times R \times 8}{100} \]
\[ 600 = 8R \implies R = \frac{600}{8} = 75\% \]

4. **Calculate the Simple Interest for 19 Times**:
- If we want to find out how long it will take for the principal to become 19 times, we first find the total amount:
\[ A = 19P = 19 \times 100 = 1900 \]
- The simple interest required to reach this amount is:
\[ SI = A - P = 1900 - 100 = 1800 \]

5. **Use the Rate to Find Time**:
- We will use the same formula for simple interest to find the time (T) it takes to earn 1800 with the same rate of interest:
\[ 1800 = \frac{100 \times 75 \times T}{100} \]
\[ 1800 = 75T \implies T = \frac{1800}{75} = 24 \text{ years} \]

### Conclusion:
It will take **24 years** for the sum to become 19 times its original amount.