A certain sum of money becomes 5 times in 15 years when…

A certain sum of money becomes 5 times in 15 years when invested at simple interest. In how much time (years and months) will it become 12 times of itself at the same rate at simple interest?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 41 years 3 months.

Amount becomes 5 times in 15 years

So, Simple Interest (SI) = 5x − x = 4x

Use SI = (P × R × T)/100

⇒(P × R × 15)/100 = 4P ⇒ R = 400/15 = 26.67%

Now: We want it to become 12 times ⇒ SI = 11x

$\frac{P \times 26.67 \times T}{100} = 11P \\ \Rightarrow \frac{26.67T}{100} = 11 \\ \Rightarrow T = \frac{1100}{26.67} \approx 41.25$

Convert 0.25 years = 0.25 × 12 = 3 months

41 years 3 months

SSC Selection Post 2022 PYQ — Question 67