CAT 2017 Slot 1 — QA Question 1
PercentageEasy
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?
Answer & solution
Answer: 20
Solution
Let Barun’s age be 10x. Arun’s age is 4x.
The difference of these ages in 6x, a constant.
When Arun’s age is 50% of Barun’s age, this difference also would be 50% i.e., Barun’s age, at that stage would be 12x.
It would be increase by 20%.
Alternately,
Let Barun’s age be 10x. Arun’s age is 4x.
In t years, Arun's age will be 50% or half of Barun's age
⇒ (4x + t) = 1/2 × (10x + t)
⇒ t = 2x
∴ Barun's age will become 12x.
⇒ Required % = (12x - 10x)/10x × 100% = 20%
Hence, 20.