Question
The average weight of x students
in a class increases by 1.5 kg when a new student of weight 69 kg joins the class. If instead, two students each weighing 62 kg join the original group, the average weight (compared to the original) increases by 2 kg. Find x.Solution
ATQ, Number of students = x Let initial average weight = y kg Total weight = xy kg First condition: (xy + 69) = (x + 1) × (y + 1.5) Or, xy + 69 = xy + y + 1.5x + 1.5 Or, y + 1.5x = 67.5 ----------- (I) Second condition: (xy + 62 × 2) = (x + 2) × (y + 2) Or, xy + 124 = xy + 2y + 2x + 4 Or, 2y + 2x = 120 So, y + x = 60 ----------- (II) From (II): y = 60 – x Substitute in (I), 60 – x + 1.5x = 67.5 0.5x = 7.5 x = 15 So, value of x = 15
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