One needs to recognize that averages and mixtures are effectively two sides of the same coin. This question is designed to drive home that point.
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Let average in class C = x. Average of class B = x +16. Average of class A = y
y = 2 + 20y+30(x+16)+50x10020y+30(x+16)+50x100
(y - 2) * 10 = 2y + 3x + 48 + 5x
10y - 20 = 2y + 8x + 48
8y - 8x = 68
y - x = 8.5. This is the difference between average of class A and class C.
The question is "This question is designed to drive home that point."
Hence, the answer is "This is the difference between average of class A and class C.".
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