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 ?

(a) 1 only
(b) 2 only ✓ UPSC's answer
(c) Both 1 and 2
(d) Neither 1 nor 2

Why the answer is (b)

• Let the present age of Y be $y$ years. Since X is currently 42, at the time of Y's birth (which was $y$ years ago), X's age was $42 - y$.

• The problem states that at Y's birth, X was twice as old as Y is now, so $42 - y = 2y$, which simplifies to $3y = 42$, giving $y = 14$. Thus, Y is currently 14 years old.

• For Statement 1: 8 years ago, X was $42 - 8 = 34$ and Y was $14 - 8 = 6$. Since $34$ is not five times $6$ ($5 \times 6 = 30$), Statement 1 is incorrect.

• For Statement 2: After 14 years, X will be $42 + 14 = 56$ and Y will be $14 + 14 = 28$. Since $56$ is exactly two times $28$, Statement 2 is correct.

• Therefore, only Statement 2 is correct, which corresponds to option (b).

Why the other options are wrong

(a) 1 only: Statement 1 is incorrect because 8 years ago, X was 34 and Y was 6, and 34 is not five times 6.
(c) Both 1 and 2: Statement 1 is incorrect, so it is false that both statements are correct.
(d) Neither 1 nor 2: Statement 2 is correct, so it is false that neither statement is correct.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.