The average weight of some persons in a group is 72 kg. When 5 persons with average weight 66.6 kg join and 13 persons with average weight 75 kg leave the group, the average weight of the personsin the group decreases by 1.65 kg. How many persons were there in the group initially?

48

5 person join the group ,

Sum of weight of 5 person = 5 × 66.6 = 333 kg

13 person leave the group ,

Sum of weight of 13 person  = 13 × 75 = 975 kg

Difference in weight = 975 - 333 = 642 kg

Let initial number of person = N

According to question ,

N × 72 - 642 = ( N - 8 ) × 70.35

72N - 642 = 70.35N - 562.8

1.65N = 79.2

N = 48

So , Initial number of person = 48