Multiple choice

The average weight of males in a family is 50 kg and the average weight of females in the same family is 40 kg. The average weight of the whole family is 42 kg. What could be the possible strength of males and females, respectively in the family?

  1. 2 and 8

  2. 2 and 10

  3. 3 and 9

  4. 4 and 12

  5. 4 and 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be the number of males and F be the number of females. (50M + 40F) / (M + F) = 42. 50M + 40F = 42M + 42F. 8M = 2F, so F = 4M. The ratio of males to females is 1:4. Option A (2 and 8) fits this ratio.

AI explanation

Using the method of alligation, the ratio of males to females equals the difference between the female average and the combined average divided by the difference between the combined average and the male average, which is (42 - 40) / (50 - 42) = 2 / 8. A ratio of 2:8 corresponds exactly to a possible strength of 2 males and 8 females.

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