Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find the value of both to find the relationship among them. Four years ago, the ratio of ages of A and B is 5 : 6 and five years after the ratio will become 6 : 7, then find- Quantity I: Present age of A. Quantity II: Age of B, 4 years ago.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and B be present ages. Four years ago: (A-4)/(B-4) = 5/6 → 6A - 24 = 5B - 20 → 6A - 5B = 4. Five years after: (A+5)/(B+5) = 6/7 → 7A + 35 = 6B + 30 → 7A - 6B = -5. Solving these equations: Multiply first by 6 (36A - 30B = 24) and second by 5 (35A - 30B = -25). Subtract to get A = 29. Then B = 35. Quantity I (A's present age) = 29. Quantity II (B's age 4 years ago) = 35 - 4 = 31. Since 31 > 29, Quantity II is greater. Option C is correct.

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