Multiple choice

The average marks of boys in a class is $52$ and the girls is $42$ . The average marks of boys and girls combined is $50$ . The percentage of boys in the class is

  1. $0$
  2. $20$
  3. $80$
  4. $60$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be the fraction of boys and G be the fraction of girls. 52B + 42G = 50(B+G). 52B + 42(1-B) = 50. 52B + 42 - 42B = 50. 10B = 8. B = 0.8, which is 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 the ratio as (50 minus 42) to (52 minus 50), which is 8 to 2 or 4 to 1. The percentage of boys is 4 divided by 5, which equals 0.8, making it 80 percent.

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