Multiple choice

Each question has two statements (I) and (II). Choose Rohit, Sameer and Vikram are three friends. Present average age of Rohit, Sameer and Vikram is 28 years. Find the present age of Vikram. I. Present average age of Sameer and Vikram is 32 years. Present age of Sameer is 25% more than the present age of Rohit. II: Present average age of Rohit and Sameer is 24 years.

  1. Statement (1) alone is sufficient

  2. Statement (2) alone is sufficient

  3. Both together are sufficient

  4. Each alone is sufficient

  5. Neither is sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R, S, V be the ages. (R+S+V)/3 = 28 => R+S+V = 84. Statement I: (S+V)/2 = 32 => S+V = 64. Then R = 84 - 64 = 20. Also S = 1.25R = 25. Then V = 64 - 25 = 39. Sufficient. Statement II: (R+S)/2 = 24 => R+S = 48. Then V = 84 - 48 = 36. Sufficient. Both are sufficient independently.

AI explanation

The total sum of the ages of all three friends is 3 times 28, which equals 84 years. Statement II gives the sum of Rohit and Sameer's ages as 2 times 24, equaling 48 years; subtracting this from 84 leaves Vikram's age as 36 years, making statement II alone sufficient. Statement I states Sameer and Vikram's average age is 32, so their sum is 64, and since Sameer's age relates to Rohit's by a 25 percent increase, you can set up the equations S plus V equals 64 and R plus S plus V equals 84 to find R equals 20, which also uniquely determines V as 36; therefore, each statement alone is sufficient.

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