The average weight of some students in a group is 58 kg. If 8 students of average weight 54 kg leave the group, and 3 students weighing 53.6 kg, 54 kg and 57.4 kg join the group, then the average weight of the remaining students in the group will increase by 575 g. The number of students, initially, in the group is:

45

3 students  join the group ,

Sum of weight of 3 students = 53.6 + 54 + 57.4 = 165 kg

8 students  leave the group ,

Sum of weight of 8 students   = 8 × 54 = 432 kg

Difference in weight = 432 - 165 = 267 kg

Let initial number of person = N

According to question ,

N × 58 - 267 = ( N - 5 ) × 58.575

58N - 267 = 58.575N - 292.875

0.575N = 25.875

N = 45

So , Initial number of person = 45