Multiple choice

Directions: In this question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. The average of the present ages of three persons X, Y and Z is 38 years. The present age of Y is 6/5 of the present age of X and the present age of Z is 160% of the present age of X. Quantity 1: 90% of the present age of X Quantity 2: 80% of the present age of Z

  1. Quantity 2 > Quantity 1

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 1 > Quantity 2

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
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A Correct answer
Explanation

Average age = 38, so X+Y+Z = 114. Y = 1.2X, Z = 1.6X. X + 1.2X + 1.6X = 3.8X = 114, so X = 30. Then Y = 36, Z = 48. Quantity 1 = 0.9 * 30 = 27. Quantity 2 = 0.8 * 48 = 38.4. Quantity 2 > Quantity 1.

AI explanation

Let the present age of X be x; then the present ages of Y and Z are 1.2x and 1.6x. Their average is 38, so (x + 1.2x + 1.6x) / 3 = 38, giving 3.8x = 114 and x = 30. Quantity 1 is 90% of 30, which is 27, and Quantity 2 is 80% of 1.6(30), which is 38.4; therefore Quantity 2 > Quantity 1.

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