Multiple choice

The average marks of boys in a class is 52 and that of girls is 42. If the combined average marks of boys and girls is 50, then the percentage of boys in the class is ___________.

  1. 80%

  2. 60%

  3. 40%

  4. 20%
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A Correct answer
Explanation

Let B be the number of boys and G be the number of girls. 52B + 42G = 50(B+G). 52B + 42G = 50B + 50G. 2B = 8G, so B/G = 4/1. The percentage of boys is B/(B+G) = 4/(4+1) = 4/5 = 80%.

AI explanation

Using the method of alligation, the ratio of boys to girls is the difference between the combined average and the girls' average to the difference between the boys' average and the combined average. This gives a ratio of 8 to 2, or 4 to 1. Out of 5 total parts, boys constitute 4 parts. Therefore, the percentage of boys in the class is 80 percent.

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