A sum of money doubles itself in 5 years at a certain rate of simple interest. In how many years will it become five times itself at the same rate of interest?

Question: A sum of money doubles itself in 5 years at a certain rate of simple interest. In how many years will it become five times itself at the same rate of interest?

Solution:
Let the Principal be P.
The amount doubles in 5 years, so Amount = 2P.
Interest (I) for 5 years = 2P - P = P.

Now, the sum needs to become five times itself, so New Amount = 5P.
Required Interest (I) = 5P - P = 4P.

We know that,
P amount of interest is earned in = 5 years.
∴ 4P amount of interest will be earned in = (5 × 4) years = 20 years.

∴ The sum of money will become five times itself in 20 years.