Multiple choice

The average marks of $48$ students in a class is $45$. The average marks of the boys in the class is $40$ and the average marks of the girls in the class is $50$. What is the ratio between the numbers of boys and the number of girls in the class?

  1. $2;1$
  2. $11:1$
  3. $1:1$
  4. $1:2$
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C Correct answer
Explanation

Let B be the number of boys and G be the number of girls. Total students = 48. Total marks = 48 * 45 = 2160. 40B + 50G = 2160. Since B + G = 48, B = 48 - G. 40(48 - G) + 50G = 2160 => 1920 - 40G + 50G = 2160 => 10G = 240 => G = 24. B = 24. Ratio B:G = 24:24 = 1:1.

AI explanation

Using the basic average formula, the total marks of all 48 students is 48 times 45, which equals 2160. Let the number of boys be b and the number of girls be g; the total marks equation is 40b + 50g = 2160. We also know b + g = 48, so multiplying this by 40 gives 40b + 40g = 1920. Subtracting this from the first equation leaves 10g = 240, meaning g = 24, and thus b = 24, making the ratio 24:24 or 1:1. The result is 1:1.

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