Multiple choice

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is Arun's present age? I. Five years ago, Arun's age was double that of his son's age at that time. II. Present ages of Arun and his son are in the ratio of 11 : 6 respectively. III.Five years hence, the respective ratio of Arun's age and his son's age will become 12 : 7.

  1. Only II and III

  2. Only I and II

  3. Only I and III

  4. Any two of the three

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

Let A and S be current ages. I: A-5 = 2(S-5). II: A/S = 11/6. III: (A+5)/(S+5) = 12/7. Any two of these equations form a system that can be solved for A and S. For example, I and II: A=11k, S=6k. 11k-5 = 2(6k-5) => 11k-5 = 12k-10 => k=5. A=55.

AI explanation

Evaluating the statements, any two of them provide two independent equations to solve for the two variables of Arun's and his son's present ages. For example, using statements I and II, let the present ages be 11x and 6x; five years ago their ratio was double, giving the equation (11x minus 5) divided by (6x minus 5) equals 2, which solves to x equaling 5. Using statements II and III gives the equation (11x plus 5) divided by (6x plus 5) equals 12 sevenths, and using statements I and III allows setting up (2x plus 5) divided by (x plus 5) equals 12 sevenths, meaning any two of the three statements are sufficient.

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