Average weight of a group of ‘x’ people increased by 1.5 kg, when a person weighing 56 kg joined the group while the average weight increased by 2 kg when two persons weighing 51 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 grouop be ‘y’ kg
Total weight of all the persons in the group = x × y = ‘xy’ kg
ATQ,
(xy + 56) = (x + 1) × (y + 1.5)
Or, xy + 56 = xy + y + 1.5x + 1.5
Or, y + 1.5x = 54.5
So, y = 54.5 – 1.5x ------------(I)
Also,
(xy + 51 × 2) = (x + 2) × (y + 2)
Or, xy + 102 = xy + 2y + 2x + 4
Or, y + x = 49 ------------ (II)
Putting value of ‘y’ from equation (I) in equation (II), we get
54.5 – 1.5x + x = 49
Or, 0.5x = 5.5
So, x = 11
So, value of ‘x’ = 11