Multiple choice

The mean weight of the students in a certain class is $60$ kg. The mean weight of the boys from the class is $70$ kg and that of the girls is $55$ kg. What is the ratio of the number of boys to that of girls?

  1. $2:1$
  2. $1:2$
  3. $1:4$
  4. $4:1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B be the number of boys and G be the number of girls. (70B + 55G) / (B + G) = 60. 70B + 55G = 60B + 60G. 10B = 5G. B/G = 5/10 = 1/2.

AI explanation

Using the method of alligation, we compare the mean weight of the boys at 70 and the mean weight of the girls at 55 against the class mean of 60. The ratio of the number of boys to girls is proportional to the differences between each group average and the combined average. The difference for the girls is 60 minus 55, which is 5, and the difference for the boys is 70 minus 60, which is 10; therefore, the ratio of boys to girls is 5 to 10, or 1 to 2.

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