The average weight of a certain numberofstudents in a group is 72 kg. If 10 students having an average weight of 78 kg leave and 4 students having an average weightof 80 kg join the group, the average weight of the students in the group decreases by 0.7 kg, The number of students initially in the group is:

Let the total number of students be n.
Sum of the weight = 72n
Average weight of 10 students = 78 kg
Sum of the weight of 10 students = 78 $$\times$$ 100 = 780
Sum of the weight of 4 students = 80 $$\times$$ 4 = 320
ATQ,
Average = sum of the terms/number of the term
$$\frac{72n - 780 + 320}{n - 10 + 4}$$ = 72 - 0.7
72n - 460 = 71.3 $$\times$$ (n - 6)
72n - 460 = 71.3n - 427.8
0.7n = 32.2
n = 46
The number of students initially in the group is 46.