Question

A sum of money triples itself in 8 years at simple interest. In how many years will it become five times itself at the same rate?

• A. 12 years
• B. 20 years
• C. 16 years
• D. 24 years

Hint:

Use the formula \( SI = \frac{PRT}{100} \) and set interest as per the multiple increase in amount.

Answer 1

The Correct Option is C

To solve the problem, we need to determine the number of years it will take for a sum of money to become five times itself under simple interest, given that it triples in 8 years.

1. Understanding the Concepts:

- Simple Interest (SI): Interest calculated on the original principal for the entire time period.
- Formula: \( \text{SI} = \frac{P \times R \times T}{100} \)
- Final Amount (A): Given by \( A = P + \text{SI} \)
- If a sum triples, it becomes \( 3P \), meaning the interest earned is \( 2P \).

2. Given Values:

- \( A = 3P \) in 8 years → SI = \( 2P \)
- Using SI formula: \( 2P = \frac{P \times R \times 8}{100} \)

3. Calculate the Rate of Interest:

\[ 2P = \frac{P \times R \times 8}{100} \Rightarrow 2 = \frac{R \times 8}{100} \Rightarrow R = \frac{200}{8} = 25\% \]

4. Use Rate to Find Time to Become 5 Times:

To become five times, SI = \( 5P - P = 4P \)
Using SI formula: \[ 4P = \frac{P \times 25 \times T}{100} \Rightarrow 4 = \frac{25T}{100} \Rightarrow T = \frac{4 \times 100}{25} = 16 \text{ years} \]

Final Answer:

The sum will become five times itself in 16 years.