The simple interest, sum of money becomes 3 times of itself in 20 rupees. In how many years does it become double of itself at same rate of interest?

8 years

10 years

12 years

None of these

Let's break it down step by step:

Let the principal amount be P.

According to the problem, the amount becomes 3 times itself in 20 years, so the interest earned is 2P (since 3P = P + 2P).

The simple interest formula is: Interest = (Principal × Rate × Time)/100

We know that Interest = 2P and Time = 20 years. Let's denote the rate as R.

So, 2P = (P × R × 20)/100

Simplifying, we get: R = 10%

Now, let's find the time it takes for the amount to become double (i.e., interest = P):

P = (P × 10 × Time)/100

Time = 10 years