Multiple choice

Directions: The following questions are accompanied by three statements A, B and C. You have to determine which statement(s) is/are sufficient necessary to answer the questions and mark your answer accordingly. What is the present age of Arun? (A) Eight years ago, age of Ankit is same as Aman's present age while four years hence, age of Ankit will be same as Arun's present age. (B) Four years ago, ratio of Aman's age and Arun's age is 4:7 (C) Present age of Arun is 60% more than present age of Aman.

  1. Any two of them

  2. Either A and B or B and C

  3. Either A or B and C together

  4. Any one of them

  5. Either A and B or A and C
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Ankit = K, Aman = M, Arun = R. (A) gives K-8 = M and K+4 = R. (B) gives (M-4)/(R-4) = 4/7. (C) gives R = 1.6M. Using A and C: R = 1.6M, K = M+8, R = K+4 = M+8+4 = M+12. So 1.6M = M+12, 0.6M = 12, M = 20, R = 32. Using A and B: K = M+8, R = K+4 = M+12. (M-4)/(M+12-4) = 4/7 => 7M-28 = 4M+32 => 3M = 60 => M=20, R=32. Both pairs (A,C) and (A,B) are sufficient.

AI explanation

Let the present ages of Ankit, Aman, and Arun be a, m, and r. Statement A yields the equations a equals m and a plus 4 equals r, providing two independent equations. Statement B provides the equation m minus 4 divided by r minus 4 equals 4 divided by 7, while statement C provides r equals 1.6 times m. Any two of these three statements provide a system of two equations in two variables, which is always sufficient to find the unique present age of Arun.

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