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)

Let the age of Rahul, Sagar and Purav be x, y and z respectively
According 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