CAT 2017 Slot 1 QA Question 2: Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?

Question

Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?

Accepted Answer

Let Barun's present age be B years. Then Arun's present age is 40% of B, i.e., $0.4B$ years.

Let the required number of years be t.
$0.4 B + t = 0.5 (B + t)$
$0.4 B + t = 0.5 B + 0.5 t$
$0.5 t = 0.1 B$
$t = 0.2 B$

So, Barun's age increases by $0.2B$ years on a base of B years.
$	ext{Required perc