Question
Average weight of a group of βxβ people increased by
2 kg, when a person weighing 70 kg joined the group, while the average weight increased by 3 kg when two persons weighing 68 kg each joined the group. Find the value of βxβ.Solution
Number of people in the group = βxβ
Let, average weight of each person in the group be βyβ kg
Total weight of all the persons in the group = x Γ y = βxyβ kg
ATQ,
(xy + 70) = (x + 1) Γ (y + 2)
Or, xy + 70 = xy + y + 2x + 2
Or, y + 2x = 68 ------------(I)
Also,
(xy + 68 Γ 2) = (x + 2) Γ (y + 3)
Or, xy + 136 = xy + 2y + 3x + 6
Or, 2y + 3x = 130 ------------(II)
Putting value of βyβ from equation (I) in equation (II), we get
y = 68 β 2x
So, 2(68 β 2x) + 3x = 130
Or, 136 β 4x + 3x = 130
Or, βx = β6
So, x = 6
So, value of βxβ = 6
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