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?

QUESTION

CSAT

Easy

Maths

Prelims 2021

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:

8 years ago, the age of X was five times the age of Y.
After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct?

Select an option to attempt

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.

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