Multiple choice

Question below contains two quantities I and II. Find the values of quantities and mark the appropriate option as your final answer. Quantity I: Respective ratio of the present ages of Aman and Bhanu is 3:4 respectively and respective ratio of the present ages of Bhanu and Chandan is 6:7 respectively. Average of the ages of Aman, Bhanu and Chandan after three years will be 20.5 years. Find the present age of Chandan. Quantity II: Present ages of Bhanu and Chandan are in the ratio of 3:4 respectively. Three years hence, the ratio of their age will become 7:9 respectively. What is the Bhanu’s present in years?

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can't be established
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A Correct answer
Explanation

Quantity I: Aman:Bhanu = 3:4 and Bhanu:Chandan = 6:7. Converting to a common ratio gives Aman:Bhanu:Chandan = 9:12:14. Let their ages be 9x, 12x, 14x. After 3 years, average age = (9x+3 + 12x+3 + 14x+3)/3 = (35x+9)/3 = 20.5. Solving gives 35x = 52.5, so x = 1.5. Chandan's present age = 14×1.5 = 21 years. Quantity II: Bhanu:Chandan = 3:4, let ages be 3x, 4x. After 3 years: (3x+3)/(4x+3) = 7/9. Cross-multiplying: 27x + 27 = 28x + 21, giving x = 6. Bhanu's present age = 3×6 = 18 years. Since 21 > 18, Quantity I > Quantity II.

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