# Rahul is as much younger than Sagar as he is older than Purav. If the sum of the ages of Purav and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Rahul and Purav's age ? ( in years)

A. 18

B. 15

C. 16

D. 20

E. Cannot be determined

**Answer: Option B **

__Solution(By Examveda Team)__

Let the age of Rahul, Sagar and Purav be x, y and z respectivelyAccording to the given information

Age of Sagar - Age of Rahul = Age of Rahul - Age of Purav

$$\eqalign{ & \Rightarrow y - x = x - z \cr & \Rightarrow 2x = y + z......(i) \cr} $$

Also y + z = 66 years

From (i) x = 33 years

Also as per equation (i) we have Purav's age + Sagar age = 66 years

by going through option (A) given Purav = 18, and Rahul = 33 years, Sagar = 48 years

Difference between Rahul's and Purav's age = 33 - 18 = 15 years

Why you consider option a

Seems it has 2 answers.

Rahul=33

If Difference is 18 then

Purav=15

Rahul=15+18=33

Sagar=33+18=51

Purav+Sagar=15+51=66

Again if Difference is 15

Then Purav=18

Rahul=18+15=33

Sagar=33+15=48

Purav+Sagar=18+48=66

Thanks Mishu, Answer updated

How difference is 18??rahul age- purav age=33-18=15

But how 18 is the answer??