Multiple choice

Directions: In the following question, two statements labelled I and II are given. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and give your answer from the given options. What is the ratio of the present ages of Deepak and Ankit? I. 10 years ago the ratio of Deepak's age to Ankit's age was 2 : 1. II. Deepak is 10 years older than Ankit.

  1. Statement I alone is sufficient, but statement II alone is not sufficient.

  2. Statement II alone is sufficient, but statement I alone is not sufficient.

  3. Both statements I and II together are sufficient, but none of the statements alone is sufficient.

  4. Either statement I or statement II alone is sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let D and A be present ages. I: (D-10)/(A-10) = 2/1 -> D-10 = 2A-20 -> D = 2A-10. II: D = A+10. Combining: A+10 = 2A-10 -> A = 20, D = 30. Ratio 30:20 = 3:2. Both are needed.

AI explanation

Statement I states that 10 years ago the ratio of Deepak's age to Ankit's age was 2 : 1, giving the equation (D - 10) / (A - 10) = 2 / 1, which simplifies to D = 2A - 10. Statement II states that Deepak is 10 years older than Ankit, giving the equation D = A + 10. Since statement I alone and statement II alone each provide only one independent equation with two variables, neither is sufficient independently, but combining them gives the complete relationship needed to find the ratio of their present ages. Therefore, both statements I and II together are sufficient, but none of the statements alone is sufficient.

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