The average height of some students in a group is 156 cm. If 5 students of average height 160 cm join the group, then the average height of all the students in the group increases by 0.8 cm. What is the number of students in the group, initially?

20

Let no. of students in a group x

Total height of x students = x × 156 = 156x cm

Total height of 5 students = 5 x 160 = 800 cm

Total height of (x + 5) students = 800 + 156x

New average = 156 + 0.8 = 156.8 cm

New number of students = x + 5

Total height of (x + 5) students = (x + 5) x 156.8 = ( 156.8x + 784) cm

⇒ 156.8x + 784 = 800 + 156x

⇒ x = 20

∴ Number of students = x = 20