Multiple choice

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer: Find the age of Arun before six years? I. Ratio of the present ages of Arun and Niketan is 4:5 respectively. Niketan is four years younger than Rishabh. II. After four years, ratio of the ages of Arun and Rishabh will be 5:7 respectively. III. Sum of the present ages of Niketan and Rishabh is 44 years.

  1. I and either II or III

  2. Only II and either I or III

  3. All I, II and III

  4. Any two of the three

  5. Even I, II and III together are not sufficient.
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A Correct answer
Explanation

Let present ages be A, N, R. From I: A/N = 4/5, N = R - 4. This gives A = (4/5)N and R = N + 4, but N is unknown. From II: (A+4)/(R+4) = 5/7, giving 7(A+4) = 5(R+4). From III: N + R = 44. Using I+III: N + (N+4) = 44, so N = 20, R = 24, A = 16. Age 6 years ago = 10. Using I+II: We have two equations in A, N, R - insufficient. Using II+III: Two equations, three unknowns - insufficient. Using I+II+III: All three work but I+III alone suffice.

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