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?

Let M_2002 and R_2002 be the ages of Meenu and Meera in 2002, respectively. Let M_2010 and R_2010 be the ages of Meenu and Meera in 2010, respectively. From the first statement: In 2002, Meenu's age was one-third of Meera's age. M_2002 = R_2002 / 3 (Equation 1) From the second statement: In 2010, Meenu's age was half the age of Meera. M_2010 = R_2010 / 2 (Equation 2) The time difference between 2002 and 2010 is 8 years. So, M_2010 = M_2002 + 8 And R_2010 = R_2002 + 8 Substitute these into Equation 2: (M_2002 + 8) = (R_2002 + 8) / 2 2 * (M_2002 + 8) = R_2002 + 8 2 * M_2002 + 16 = R_2002 + 8 From Equation 1, we know R_2002 = 3 * M_2002. Substitute this into the above equation: 2 * M_2002 + 16 = (3 * M_2002) + 8 Now, solve for M_2002: 16 - 8 = 3 * M_2002 - 2 * M_2002 8 = M_2002 So, Meenu's age in 2002 was 8 years. To find Meenu's year of birth, subtract her age in 2002 from the year 2002: Year of birth = 2002 - 8 = 1994. Analyzing the options: A) 1992: Incorrect. If born in 1992, Meenu would be 10 in 2002. B) 1994: Correct. If born in 1994, Meenu would be 8 in 2002. C) 1996: Incorrect. If born in 1996, Meenu would be 6 in 2002. D) 1998: Incorrect. If born in 1998, Meenu would be 4 in 2002. The final answer is B.