Q. X said to Y, “At the time of your birth I was twice as old as you are at present.” If the present age of X is 42 years, then consider the following statements:

Explanation : 

X & Y Age Relationship Analysis

Let’s say Y’s present age is y and X’s present age is 42. According to the given information, at the time of Y’s birth, X was twice as old as Y is now. So we can write the equation: 42-y = 2y. Solving for y gives us y = 14.

Now let’s check statement 1: “8 years ago, the age of X was five times the age of Y.” Eight years ago, X was 42-8 = 34 years old and Y was 14-8 = 6 years old. Since 34 is not equal to five times six (30), statement one is incorrect.

Now let’s check statement 2: “After 14 years, the age of X would be two times the age of Y.” In fourteen years’ time, X will be 42+14 =56 years old and Y will be 14+14=28 years old. Since two times twenty-eight (56) equals fifty-six (56), statement two is correct.

So only statement two is correct and therefore option (b) “2 only” is the correct answer.