Question
The total number of teachers in
Department A and Department B together is 112. The number of teachers in Department A is 80% more than the number of teachers in Department B. The average weight (in kg) of the teachers in Department A is 40% more than the average weight (in kg) of the teachers in Department B. If the average weight of all the teachers in both departments combined is 88 kg, what is the average weight of the teachers in Department A?Solution
ATQ, Let number of teachers in Department B = ‘x’ Number of teachers in Department A = 1.80 × x = 1.8x So, 1.8x + x = 112 Or, 2.8x = 112 Or, x = 40 Number of teachers in Department B = 40 Number of teachers in Department A = 1.8 × 40 = 72 Let average weight of teachers of Department B = ‘y’ kg Average weight of teachers of Department A = 1.40 × y = 1.4y kg According to question; (40 × y + 1.4y × 72)/112 = 88 Or, 40y + 100.8y = 88 × 112 Or, 140.8y = 88 × 112 So, y = 70 Average weight of teachers in Department A = 1.4y = 1.4 x 70 = 98 kg
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