Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine the relationship between the two quantities and choose the appropriate option: Quantity I: The average age of four brothers W, X, Y, and Z is 27 years. The ratio of the age of W 2 years hence and the age of X 4 years hence is 9:7 respectively, and the ratio of the age of Y 4 years before and the age of Z 6 years before is 3:2 respectively. Find the age of Y if X is 2 years older than Z. Quantity II: The average age of five brothers A, B, C, D, and E is 30 years. The ratio of the age of A 5 years hence and the age of B 7 years ago is 7:5 respectively, and the ratio of the age of C and the age of D is 3:2 respectively. Find the age of E if E is 2 years younger than A and 4 years older than D.

  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 relationship cannot be established
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E Correct answer
Explanation

Quantity I: Total age = 108. Let ages be W, X, Y, Z. (W+2)/(X+4) = 9/7, (Y-4)/(Z-6) = 3/2, X = Z+2. This gives 7W+14 = 9X+36 and 2Y-8 = 3Z-18. With W+X+Y+Z = 108 and X = Z+2, we have 4 equations with 4 unknowns, but solving gives inconsistent results for Y. Quantity II: Total age = 150. Multiple constraints also give indeterminate values for E. Both quantities cannot be uniquely determined from given information.

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