Multiple choice

Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: There are 42 workers in a factory with an average weight of 65 kg. The ratio of the number of male workers to female workers is 13: 8. If the average weight of male workers and female workers is 72 kg and ‘x’ kg respectively, then find the value of ‘x’. Quantity II: The average weight of a class of 25 students is ‘x’ kg. If a student whose weight is 100 kg is excluded, then the average of the class reduces by 2 kg. Find the value of ‘x’.

  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 No relation
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A Correct answer
Explanation

Quantity I: Total weight = 42 × 65 = 2730 kg. Male:Female = 13:8, so Males = (13/21)×42 = 26, Females = 16. Male weight = 26 × 72 = 1872 kg. Female weight = 2730 - 1872 = 858 kg. Female average = 858/16 = 53.625 kg. Quantity II: Original average = x, total = 25x. After removing 100kg student: New average = x - 2, new total = 24(x - 2) = 24x - 48. So 25x - 100 = 24x - 48, giving x = 52. Since 53.625 > 52, Quantity I > Quantity II.

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