In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth ?
- (a) 1992
- (b) 1994 ✓ UPSC's answer
- (c) 1996
- (d) 1998
Why the answer is (b)
• Let Meenu's age in 2002 be $x$ and Meera's age be $y$.
• The first condition gives the equation $x = \frac{1}{3}y$, or $y = 3x$.
• In 2010 (8 years later), Meenu's age is $x + 8$ and Meera's age is $y + 8$.
• The second condition gives the equation $x + 8 = \frac{1}{2}(y + 8)$.
• Substituting $y = 3x$ into the second equation: $x + 8 = \frac{1}{2}(3x + 8)$.
• Solving yields $2x + 16 = 3x + 8$, so $x = 8$.
• Meenu was 8 years old in 2002, so her birth year is $2002 - 8 = 1994$.
Why the other options are wrong
- (a) 1992
- This option corresponds to a birth year of 1992, implying Meenu was 10 in 2002, which does not satisfy the ratio conditions.
- (c) 1996
- This option corresponds to a birth year of 1996, implying Meenu was 6 in 2002, which does not satisfy the ratio conditions.
- (d) 1998
- This option corresponds to a birth year of 1998, implying Meenu was 4 in 2002, which does not satisfy the ratio conditions.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.