Solution :

Let us take Rohit's age as 'x'  and 

Ankit's age as 'y'.

It is given that the sum of Rohit's and Ankit's age is 78.So, 

x + y = 78 -------------------> 1

Also, Rohit's age is twice the age of Ankit's so,

x = 2y ---------------------> 2

Substituting 2 in 1 we get,

2y + y = 78

3y = 78

y = 78/3

y = 26

Substituting the value of y in eqn 2 we get,

x = 2×26

x = 52

So, Rohit's age is 52 

The correct option is 2). 52