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?
Answer & explanation
Answer: (b) 2 only
X's age at Y's birth is the age gap X − Y, which equals twice Y's present age; so X = 3Y and Y = 14. Eight years ago they were 34 and 6 (not five times), but in 14 years they will be 56 and 28 (exactly twice).
- At Y's birth X's age was X − Y, and this equals 2Y, so X = 3Y.
- X = 42, so Y = 14.
- Statement 1: 8 years ago X was 34 and Y was 6; 5 × 6 = 30, not 34. Incorrect.
- Statement 2: after 14 years X will be 56 and Y 28; 56 = 2 × 28. Correct.
- ✗ 1. 34 is not five times 6.
- ✓ 2. 56 is exactly twice 28.
Remember · 'My age at your birth' is simply the age difference, which never changes.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·