The average weight of a certain number of students in a group is 72 kg. If 10 students having an average weight of 78 kg leave and 4 students having an average weight of 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:

A. 56

B. 46

C. 44

D. 54

Answer: Option B

Solution(By Examveda Team)

Let the number of students = x
Average of x students = 72
Total weight = 72x
Change in weight
= 10 × 78 - 4 × 80
= 460
Now, total students = x - 6
$$\eqalign{ & {\text{Average}} = \frac{{72x - 460}}{{x - 6}} \cr & 71.3 = \frac{{72x - 460}}{{x - 6}} \cr & 0.7x = 32.2 \cr & x = 46 \cr} $$