Multiple choice

The average age of children in a group is 11 years. If the average age of boys is 11.2 years and that of the girls is 10.9 years, then how many children are there in the group? (Given that there are 50 boys)

  1. 50

  2. 100

  3. 150

  4. 175

  5. 195
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let G be the number of girls. Total average = 11. (11.2 * 50 + 10.9 * G) / (50 + G) = 11. 560 + 10.9G = 550 + 11G. 10 = 0.1G, so G = 100. Total children = 50 + 100 = 150.

AI explanation

Using the allegation method, the ratio of the number of boys to the number of girls is calculated from their average ages. The ratio is (11 minus 10.9) to (11.2 minus 11), which simplifies to 0.1 to 0.2, or 1 to 2. Since there are 50 boys representing 1 part of the ratio, there must be 100 girls representing 2 parts. The total number of children in the group is 50 boys plus 100 girls. The result is 150 children.

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