Multiple choice

There are five boxes in a box hold. The weight of the first box is 40 kg and the weight of the second box is 50% higher than the weight of the third box, whose weight is 25% higher than the first boxes' weight. The fourth box at 150 kg is 50% heavier than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.

  1. 21.5 kg

  2. 25 kg

  3. 27.5 kg

  4. 22.5 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Box 1 = 40. Box 3 = 40 * 1.25 = 50. Box 2 = 50 * 1.5 = 75. Box 4 = 150. Box 5 = 150 / 1.5 = 100. Weights: 40, 50, 75, 100, 150. Four heaviest: 50, 75, 100, 150 (Avg = 375/4 = 93.75). Four lightest: 40, 50, 75, 100 (Avg = 265/4 = 66.25). Difference = 93.75 - 66.25 = 27.5.

AI explanation

To maximize the average of B, the 5 highest-scoring students from A must transfer to B. Since the total marks for A are 400 and the highest score is 22, the five highest possible individual scores in A are 22, 22, 22, 22, and 12, which sum to 100. The new total marks for B become 625 plus 100, equaling 725, and the total number of students becomes 30. The maximum possible average for B is 725 divided by 30, which equals 24.5.

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