Multiple choice

The mean weight of $60$ students in a class is $40$ kg. The mean weight of boys is $50$ kg while that of the girls is $30$ kg. The number of boys and girls respectively are ___________.

  1. $30, 30$
  2. $35, 25$
  3. $25, 35$
  4. $20, 40$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B be boys and G be girls. B+G=60. 50B + 30G = 40 * 60 = 2400. 50B + 30(60-B) = 2400 => 20B = 600 => B=30, G=30.

AI explanation

Using the method of alligation, the ratio of the number of boys to girls is inversely proportional to the ratio of the deviations of their means from the combined mean. The overall mean is 40, the boys' mean is 50, and the girls' mean is 30. The ratio of boys to girls is (40 - 30) : (50 - 40), which equals 10 : 10 or 1 : 1. Applying this ratio to the total of 60 students results in 30 boys and 30 girls.

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