School X has 3 classes, A, B and C. The average score of Class B is 16 more…

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School X has 3 classes, A, B and C. The average score of Class B is 16 more than the average score of class C. The strengths of Classes A, B and C are in the ratio 2:3:5, respectively. If the average score of the school 2 less than the average score of Class A, Find the difference between average of class A and class C.

  1. A.

    8.5

  2. B.

    5

  3. C.

    7.5

  4. D.

    11.5

Attempted by 10 students.

Show answer & explanation

Correct answer: A

Let the average of class C be x and the average of class A be y.

Then the average of class B is x + 16.

Let the class sizes be 2k, 3k and 5k (ratio 2:3:5). The weighted school average is

Weighted average = (2y + 3(x + 16) + 5x) / 10

Given the school average is 2 less than class A:

(2y + 3(x + 16) + 5x) / 10 = y - 2

Multiply both sides by 10: 2y + 8x + 48 = 10y - 20

Rearrange: 8y - 8x = 68, so y - x = 8.5

Answer: The difference between the average of class A and class C is 8.5.

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