Multiple choice

Shikha and Riya are friends and their ages differ by $2$ years. Shikha's father Rajiv is twice as old as Shikha and Riya is twice as old as her sister Maya. The age of Rajiv and Maya differ by 40 years Then the age of Shikha and Riya respectively are _______

  1. $26$ years, $24$ years
  2. $\displaystyle 27\frac{1}{3}$ years, $\displaystyle 29\frac{1}{3}$ years
  3. $27$ years, $29$ years

  4. Both (A) and (B)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Shikha be S, Riya be R. |S-R|=2. Rajiv=2S, Maya=R/2. Rajiv-Maya=40 => 2S - R/2 = 40 => 4S - R = 80. If S=R+2, 4(R+2)-R=80 => 3R=72 => R=24, S=26. If R=S+2, 4S-(S+2)=80 => 3S=82 => S=27.33, R=29.33. Both cases are valid.

AI explanation

Let Shikha's age be S, making Riya's age either S + 2 or S - 2, Rajiv's age 2S, and Maya's age half of Riya's. The difference between Rajiv's age and Maya's age is 40, creating two valid cases based on the age gap. In the first case where Riya is older, (2S) - (S + 2)/2 = 40, which solves to S = 27 and Riya = 29. In the second case where Shikha is older, (2S) - (S - 2)/2 = 40, which solves to S = 26 and Riya = 24. Therefore, both sets of ages are valid.

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