Multiple choice

Let the average score of a class of boys and girls in an examination be p. The ratio of boys and girls in the class is 3 : 1. If the average score of the boys is (p + 1), then what is the average score of the girls?

  1. (p - 1)

  2. (p - 2)

  3. (p - 3)

  4. p
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be the number of boys and G be the number of girls. B:G = 3:1. Total students = 4. Average = (3(p+1) + 1*x) / 4 = p. 3p + 3 + x = 4p. x = p - 3.

AI explanation

Let the number of boys be 3x and the number of girls be x. The total score of the class is (3x + x) * p = 4px. The total score of the boys is 3x * (p + 1) = 3px + 3x. If the average score of the girls is G, their total score is x * G. Using the method of alligation or equating totals, 4px = 3px + 3x + xG. Solving for G, we get xG = 4px - 3px - 3x = px - 3x. Dividing by x yields G = p - 3, so the average score of the girls is (p - 3).

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