Multiple choice

The average score of the 25 boys in a class is 34 and the average score of the girls in the same class is 42. If the average score of the whole class (boys and girls together ) is 37. How many girls are there in the class?

  1. 30

  2. 15

  3. 24

  4. 18

  5. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B be the number of boys (25) and G be the number of girls. Total score = 25 * 34 + G * 42 = (25 + G) * 37. 850 + 42G = 925 + 37G. 5G = 75, so G = 15.

AI explanation

Using the method of alligation, the ratio of the number of boys to the number of girls is determined by the difference between the girls' average and the overall average compared to the difference between the boys' average and the overall average. Calculate the differences as (42 - 37) for the boys and (37 - 34) for the girls, which yields 5 and 3 respectively, establishing a ratio of 5 boys to 3 girls. Given that there are 25 boys in the class, divide 25 by 5 to find the value of one ratio unit, and then multiply that result of 5 by 3 to find that there are 15 girls.

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