Multiple choice

There are four people P, Q, R, and S in a room. If a person T joins them, the average weight of everyone in the room decreases by y kg. However, if person U joins instead of T, the average weight increases by 3y kg. If the weight of U is 40 kg more than the weight of T, then what is the value of y?

  1. 1.0

  2. 1.5

  3. 2.0

  4. 2.5

  5. 3.0
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial sum be S, number of people = 4. Average = S/4. (S+T)/5 = S/4 - y. (S+U)/5 = S/4 + 3y. Subtracting: (U-T)/5 = 4y. Given U-T = 40, so 40/5 = 4y. 8 = 4y, so y = 2.

AI explanation

Let the average weight of the four people be A and the weight of person T be Wt. When T joins, the average decreases by y kilograms, meaning the total weight becomes 4(A - y) + Wt, which also equals 5(A - y); this gives Wt = A - 5y. When person U joins, whose weight is Wt + 40, the average increases by 3y, meaning the total weight is 4(A + 3y) + Wt + 40, which also equals 5(A + 3y); substituting Wt gives 4A + 12y + A - 5y + 40 = 5A + 15y. Solving 5A + 7y + 40 = 5A + 15y results in 8y = 40, yielding a value of 2.0 for y.

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