Multiple choice

In St. John's Primary school, there are two sections, A and B, in class I each consisting of equal number of students. The average weight of the students in section A and section B are 44 kg and 50 kg, respectively. If one-fifth of the students in section B are moved to section A, the average weight of the students in section A increases by 1 kg. Which of the following is true regarding the average weight of the students in section B after the movement of students to section A?

  1. Decreases

  2. Remains unchanged

  3. Increases

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the number of students in each section. Total weight A = 44n, B = 50n. Moving 1/5n students (average 50) to A: New total weight A = 44n + 0.2n * 50 = 54n. New count A = 1.2n. New average A = 54n / 1.2n = 45. This matches the increase of 1 kg. For B, removing 1/5n students with average weight 50 from a group with average weight 50 leaves the average unchanged.

AI explanation

When students are moved from one group to another without changing the overall composition, the total weight remains constant. Let the number of students in section B be 5x, meaning one-fifth is x students. Moving these x students (who have an average weight of 50 kg) into section A takes exactly 50x kg of total weight away from section B. The new average weight of section B is calculated by dividing the remaining total weight, which is 50 times 5x minus 50x, by the new number of students, 5x minus x. This gives 200x divided by 4x, which equals 50 kg, proving the average remains unchanged.

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