Multiple choice

Which of the given statements is/are necessary/required to answer the question. What is the present age of Sameer? I. The present age of Sameer is half of his father’s age. II. After five years, the ratio of ages of Sameer and his father will be 6:11. III. 10 years ago age of father was 266.67% of the age of Sameer at that time.

  1. Only I and II

  2. Only I and III

  3. I and (II or III)

  4. All together are not sufficient

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let Sameer's age be S, father's age be F. Statement I: S = F/2. Statement II: (S+5)/(F+5) = 6/11. Cross-multiplying: 11S + 55 = 6F + 30. Using I (F=2S): 11S + 55 = 12S + 30, so S = 25. With I and II, we get S=25, F=50. Statement III: 10 years ago, F-10 = 266.67% of (S-10). This is equivalent to (F-10) = 8/3 × (S-10), which simplifies to information consistent with I. Since I and II give a unique answer and option E says 'None of these' (meaning none of A-D), the claimed answer is correct.

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