Multiple choice

In a co-ed class, average weight of the students is 50 kg. Average weight of boys is 55 kg and average weight of girls 45 kg. If there are 30 boys in the class, then how many girls are there in the class?

  1. 30

  2. 25

  3. 20

  4. 35

  5. 40
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A Correct answer
Explanation

Let G be the number of girls. The total weight is 50(30 + G). The sum of weights is 55(30) + 45(G). Setting them equal: 1500 + 50G = 1650 + 45G. Solving for G gives 5G = 150, so G = 30.

AI explanation

Using the method of alligation, the ratio of the difference between the boys' average and the class average to the difference between the class average and the girls' average is (55 - 50) : (50 - 45), which simplifies to 5 : 5 or 1 : 1. Because this ratio represents the number of girls to the number of boys, there are exactly as many girls as boys. Since there are 30 boys, there must be 30 girls.

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