Question

A sum of money triples itself in 3 years at simple interest. In how many years will it become 9 times of itself?

• A. 9 years
• B. 10 years
• C. 12 years
• D. 8 years

Answer 1

The Correct Option is C

Given that a sum of money triples itself in 3 years at simple interest, we are to find out in how many years it will become 9 times of itself.

Let's denote the principal amount as \( P \). After 3 years, the sum triples, so we have:

\( 3P = P + \text{Simple Interest in 3 years} \).

This implies the simple interest for 3 years is \( 2P \).

Since simple interest \( I = \frac{P \times R \times T}{100} \), we have:

\( 2P = \frac{P \times R \times 3}{100} \).

Solving for \( R \), we get:

\( R = \frac{200}{3} \% \).

Now, we need to find out when the amount becomes 9 times. Thus,

\( 9P = P + \text{Simple Interest in \( T \) years} \)

which implies the simple interest is \( 8P \).

Using the formula: \( 8P = \frac{P \times \frac{200}{3} \times T}{100} \)

Simplifying, we get:

\( T = 12 \) years.

Therefore, the sum of money will become 9 times of itself in 12 years. The correct answer is 12 years.