A sum becomes 3 times in 5 years at compound interest. In how many years the same sum will became 9 times?

Options

A. 5
B. 10
C. 15
D. 20

Answer

To solve the problem, we need to determine how long it will take for a sum of money to become nine times its original amount at compound interest, given that it becomes three times its original amount in five years.

### Step-by-Step Solution:

1. **Understand the Problem**:
- We know that a sum of money (let's call it P) becomes three times its original amount in 5 years. This means:
\[ A = 3P \]
- We need to find out how many years it will take for the same sum to become nine times its original amount:
\[ A = 9P \]

2. **Identify the Relationship**:
- The relationship between the amount and time in compound interest can be understood as follows:
- If the amount becomes three times in 5 years, then it can be inferred that it will take another 5 years to become nine times.
- This is because:
\[ 3P \text{ (after 5 years)} \rightarrow 9P \text{ (after another 5 years)} \]

3. **Calculate the Total Time**:
- Since it takes 5 years to go from P to 3P, and another 5 years to go from 3P to 9P, the total time taken will be:
\[ 5 \text{ years} + 5 \text{ years} = 10 \text{ years} \]

4. **Conclusion**:
- Therefore, the time taken for the sum to become nine times its original amount is **10 years**.

### Final Answer:
The sum will become nine times in **10 years**.