A sum of money amounts to 3 times the original sum in 15 years. In how many years will the original sum amount to 5 times of itself at the same rate of simple interest?

Correct option is D

Given:

A sum becomes 3 times the original in 15 years

We need to find in how many years the sum becomes 5 times itself at the same rate

Formula Used:

SI = $$\frac{P\times R\times T}{100}$$​​

Solution:

Finding rate;

​$$2P = \frac{P \times R \times 15}{100} \\ \ \\ R = \frac{200}{15} = \frac{40}{3} \%$$​​

Now,

​$$4P = \frac{P \times \frac{40}{3} \times T}{100}$$​​

​$$4P = \frac{P \times 40 \times T}{300} \\ \ \\ 4 = \frac{40T}{300} \\ \ \\ 4 = \frac{2T}{15} \\ \ \\ T = \frac{4 \times 15}{2} = 30 \ year$$​​