Average weight of a group of ‘x’ 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 ‘x’.

Number of people in the group = ‘x’
Let, average weight of each person in the group be ‘y’ kg
Total weight of all the persons in the group = x × y = ‘xy’ kg
ATQ,
(xy + 70) = (x + 1) × (y + 2)
Or, xy + 70 = xy + y + 2x + 2
Or, y + 2x = 68 ------------(I)
Also,
(xy + 68 × 2) = (x + 2) × (y + 3)
Or, xy + 136 = xy + 2y + 3x + 6
Or, 2y + 3x = 130 ------------(II)
Putting value of ‘y’ from equation (I) in equation (II), we get
y = 68 – 2x
So, 2(68 – 2x) + 3x = 130
Or, 136 – 4x + 3x = 130
Or, –x = –6
So, x = 6
So, value of ‘x’ = 6