Multiple choice

In a group of junior basketball players, the average weight of boys is 65.9 kg and the average weight of girls is 57 kg. When the average weight of both boys and girls is 60.3 kg and the total number of boys in the group is 66, then what is the total number of girls in the group?

  1. 112

  2. 154

  3. 162

  4. 168

  5. 180
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A Correct answer
Explanation

Using alligation: Boys (65.9), Girls (57), Mean (60.3). Boys ratio = 60.3 - 57 = 3.3. Girls ratio = 65.9 - 60.3 = 5.6. Ratio Boys:Girls = 3.3:5.6 = 33:56. If 33 units = 66 boys, then 1 unit = 2 boys. Girls = 56 * 2 = 112.

AI explanation

Using the method of alligation, the ratio of boys to girls is the difference between the overall average and the girls' average to the difference between the boys' average and the overall average. This gives the ratio as (60.3 minus 57.0) to (65.9 minus 60.3), which simplifies to 3.3 to 5.6, or 33 to 56. Since 66 boys represent 33 parts, 1 part equals 2 people; therefore, the 56 parts for the girls equals 112 girls.

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