Discussion

Question:

In a class, there are three divisions A, B and C. The average marks in Mathematics in three divisions are 55, 40, 60 respectively whereas the weighted average of three division is 55. What is the ratio of number of students in section B and C?

Explanation:

Let the number of students in three section be a, b and c.

⇒ $\frac{55 a + 40 b + 60 c}{a + b + c}$ =55

⇒ 55a + 40b + 60c = 55a + 55b + 55c

⇒ 40b + 60c = 55b + 55c

⇒ 5c = 15b

⇒ b : c = 1 : 3

Alternately,

Since, the average of section A is same as the combined average of the three division, even if we remove section A, the combined average of other two will not change.

Hence, weighted average of section B and C is also 55.

⇒ $\frac{40 b + 60 c}{b + c}$ = 55

⇒ 40b + 60c = 55b + 55c

⇒ 5c = 15b

⇒ b : c = 1 : 3

Hence, option (b).

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