Multiple choice

The average weight of $A, B$ and $C$ is $x$ kg. $A$ and $C$ lose $y$ kg each after dieting and $B$ puts on $y/2$ kg. After this, their average weight decreases by 1 kg. Find $y$.

  1. 1.5 kg

  2. 3 kg

  3. 2 kg

  4. 3.5 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial sum = 3x. New sum = (A-y) + (B+y/2) + (C-y) = A+B+C - 1.5y = 3x - 1.5y. New average = (3x - 1.5y)/3 = x - 0.5y. Given the average decreases by 1, 0.5y = 1, so y = 2.

AI explanation

Using the method of average deviation, the total required weight decrease for A, B, and C is 3 kg times 1 kg each, which equals 3 kg. The net change in their total weight from the dieting is a loss of y kg for A, a loss of y kg for C, and a gain of y/2 kg for B, giving a net loss of 2y - y/2 = 1.5y kg. Equating this net loss to the required 3 kg total decrease gives 1.5y = 3, so y = 2. The result is 2 kg.

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