Multiple choice

The average score of boys in an examination of a school is $71$ and that of girls is $73$. The average score of the school in that examination is $71.8$. The ration of the number of boys to the number of girls appeared in the examination, is

  1. $3:2$
  2. $3:4$
  3. $1:2$
  4. $2:1$
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A Correct answer
Explanation

Let B be number of boys and G be number of girls. (71B + 73G) / (B + G) = 71.8. 71B + 73G = 71.8B + 71.8G. 1.2G = 0.8B. B/G = 1.2/0.8 = 3/2.

AI explanation

Using the method of alligation, place the boys' average of 71 and the girls' average of 73 on the left. Place the combined school average of 71.8 in the middle. The ratio of the number of boys to girls is calculated by the differences (73 - 71.8) and (71.8 - 71), which gives 1.2 to 0.8. Multiplying both sides by 10 to remove the decimals results in the ratio 12 to 8, which simplifies to 3 to 2.

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