X said 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:

Correct Option (B)

Let the present age of Y be 't' years. The present age of X is given as 42 years.

According to the statement, "At the time of your birth I was twice as old as you are at present."

• The age of X at the time of Y's birth can be expressed as the present age of X minus the present age of Y: $42-t$.
• This age was twice Y's present age: $2t$.
• Equating these two expressions: $42-t=2t$.
• Solving for t: $42=3t\Rightarrow t=\frac{42}{3}=14$ years.
• Therefore, the present age of Y is 14 years.

Evaluating Statement 2: "After 14 years, the age of X would be two times the age of Y."

• Age of X after 14 years = $42+14=56$ years.
• Age of Y after 14 years = $14+14=28$ years.
• Comparing their ages: $56=2\times 28$. This relationship holds true.
• Thus, Statement 2 is correct.

Incorrect Options:

Evaluating Statement 1: "8 years ago, the age of X was five times the age of Y."

• Age of X eight years ago = $42-8=34$ years.
• Age of Y eight years ago = $14-8=6$ years.
• Comparing their ages: $34\ne 5\times 6$, as $5\times 6=30$.
• Thus, Statement 1 is incorrect because 34 is not equal to 30.