TheCATExam
Sign in

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

Correct answer: 20

Answer: 20

Solution

Easy

The age difference between two people never changes. Pin both ages to a convenient common multiple, track the constant difference, and read off Barun's growth.

1

Set up present ages. Arun is 40%40\% of Barun, so let Barun be 10x10x and Arun be 4x4x.

Barun=10x,Arun=4x⇒ difference=10x−4x=6x(stays constant over time)\begin{aligned} &\text{Barun} = 10x,\quad \text{Arun} = 4x\\ &\Rightarrow\ \text{difference} = 10x - 4x = 6x \quad\text{(stays constant over time)} \end{aligned}
2

Use the future condition. Later Arun is half of Barun, so Arun and the difference are each 50%50\% of Barun — i.e. Arun equals the difference 6x6x.

Arunnew=difference=6x(half = the other half = difference)⇒ Barunnew=6x+6x=12x\begin{aligned} &\text{Arun}_{\text{new}} = \text{difference} = 6x \quad\text{(half = the other half = difference)}\\ &\Rightarrow\ \text{Barun}_{\text{new}} = 6x + 6x = 12x \end{aligned}
3

Percentage increase in Barun's age. From 10x10x to 12x12x.

12x−10x10x×100%=2x10x×100%(from steps 1 and 2)⇒ 20%\begin{aligned} &\frac{12x - 10x}{10x}\times 100\% = \frac{2x}{10x}\times 100\% \quad\text{(from steps 1 and 2)}\\ &\Rightarrow\ 20\% \end{aligned}
20%20\%

Algebraic check: in tt years 4x+t=12(10x+t)⇒t=2x4x+t=\tfrac12(10x+t)\Rightarrow t=2x, so Barun grows from 10x10x to 12x12x, a 20%20\% rise.

Related Percentage questions

See all Percentage questions →
CAT 2017 Slot 1 QA Q1: 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 wh — Solution | TheCATExam