Multiple choice

Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question. Question: Age of Abhay is 5 year more than Akhil's age. What is the sum of their present age? Statements: I. Ratio of their present age is 2:3. II. Akhil's age is 4 year less than their average age.

  1. Statement I alone is sufficient.

  2. Statement II alone is sufficient.

  3. Either of the statement I alone or statement II alone is sufficient.

  4. Both the statements I and II together are needed.
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A Correct answer
Explanation

Statement I gives the ratio 2:3. If Abhay's age is 3x and Akhil's is 2x, then 3x = 2x + 5, so x = 5. Their ages are 10 and 15, making the sum 25. This is sufficient. Statement II says Akhil's age is 4 less than their average. The average equals (Abhay + Akhil)/2 = (Akhil + 5 + Akhil)/2 = Akhil + 2.5. Setting Akhil = Akhil + 2.5 - 4 gives 0 = -1.5, a contradiction. Therefore Statement II is inconsistent and cannot be used.

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