The average height of a certain number of students in a group is 155.6 cm. If 12 students having an average height of 150.5 cm join the group and7  students having an average height of 159 cm leave the group, the average height of the students in the group will decrease by 34 mm . What is the number of students, initially, in the group?

20

12 students  join the group ,

Total height increased by  = 12 × 150.5 = 1806 cm

7 students  leave the group ,

Total height decreased by   = 7 × 159 = 1113 kg

Change in height  = 1806  - 1113  = 693 cm

Let initial number of person = N

According to question ,

N × 155.6 + 693 = ( N + 5 ) × 152.2

155.6N + 693  = 152.2N +  761

3.4N = 68

N = 20

So , Initial number of person = 20