Multiple choice

There are 100 persons in 3 categories A, B and C in a Wrestling competition. The average weight of all the categories was 84. The average of B and C was 87.5 and the average weight of A is 70. The number of persons in A was

  1. 20

  2. 35

  3. 30

  4. 25
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A Correct answer
Explanation

Let persons in A be 'a'. Then persons in B+C = (100-a). Total weight = 100 × 84 = 8400. Weight of A = 70a. Weight of B+C = 87.5(100-a) = 8750 - 87.5a. Equation: 70a + 8750 - 87.5a = 8400, giving -17.5a = -350, hence a = 20.

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