X said to Y quot At the time of your birth I was twice as old as you are at present quot If the pres...........

Math and Mental Ability Problems based on Ages

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?

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1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Explanation:

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.