Question
The average weight of a group of
'x' friends increased by 1 kg when a person weighing 61 kg joined them. Later, when two more persons weighing 60 kg and 58 kg joined the same original group, the average weight (compared to the original average) increased by 1.5 kg. Find the value of 'x'.Solution
ATQ, Number of friends in the group = x Let the average weight of each friend be y kg Total weight of the group = x × y = xy kg First condition: (xy + 61) = (x + 1) × (y + 1) Or, xy + 61 = xy + y + x + 1 Or, y + x = 60 ----------- (I) Second condition: (xy + 60 + 58) = (x + 2) × (y + 1.5) Or, xy + 118 = xy + 2y + 1.5x + 3 Or, 2y + 1.5x = 115 ----------- (II) From (I): y = 60 – x Putting in (II), 2(60 – x) + 1.5x = 115 120 – 2x + 1.5x = 115 120 – 0.5x = 115 0.5x = 5 x = 10 So, value of x = 10
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