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)

• When Y was born, X's age was X − Y. We are told X − Y = 2Y, so 42 − Y = 2Y and Y = 14.

• Statement 1: 8 years ago X was 34 and Y was 6; 34 is not 5 × 6 = 30, so it is not correct.

• Statement 2: after 14 years X will be 56 and Y will be 28; 56 = 2 × 28, so it is correct.

• Hence 2 only, option (b).

Why the other options are wrong

(a) 1 only: Statement 1 is wrong: 8 years ago X was 34 and Y was 6, and 34 ≠ 5 × 6.
(c) Both 1 and 2: Only statement 2 holds; statement 1 fails (34 ≠ 30).
(d) Neither 1 nor 2: Statement 2 is correct: in 14 years X will be 56 and Y 28.

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.