Step 1: Define Variables

Let: M = Meera's age in 2002 m = Meenu's age in 2002

Step 2: Set Up Equations

In 2002, Meenu's age was one-third of Meera's age: $m = \frac{M}{3}$ In 2010, Meenu's age was half of Meera's age: In 2010, Meera's age = $M + 8$ In 2010, Meenu's age = $m + 8$ According to the problem: $(m + 8) = \frac{1}{2} \times (M + 8)$

Step 3: Solve the Equations

Substitute $m = \frac{M}{3}$ into the second equation: $(\frac{M}{3} + 8) = \frac{1}{2} \times (M + 8)$ Multiply both sides by 6 to eliminate the denominators: $2(M + 24) = 3(M + 8)$

Expand both sides: $2M + 48 = 3M + 24$

Simplify: $48 - 24 = 3M - 2M$

$24 = M$

Step 4: Calculate Meenu's Age and Year of Birth Meera's age in 2002 = $M = 24$ years Meenu's age in 2002 = $m = \frac{M}{3} = \frac{24}{3} = 8$ years Meenu's year of birth = $2002 - 8 = 1994$