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:

1. 8 years ago, the age of X was five times the age of Y.

2. After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct?

Present age of X is 42 years. Let the present age of Y be y years.

As per the question, 42 – y = 2y

Or 3y = 42
Or y = 14 years

So, at present the ages of X and Y are 42 and 14 respectively.

Statement 1: Eight years ago, the ages of X and Y must have been 34 and 6 respectively.

We can see that the age of X was not 5 times the age of Y. Hence, this statement is incorrect.

Statement 2: After fourteen years, the ages of X and Y will be 56 and 28 respectively.

We can see that the age of X would indeed be two times the age of Y. Hence, this statement is correct.