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?

Let initial students = n, average = 156. Total height = 156n. 5 new students with average 160 cm join, so their total = 5 × 160 = 800. New average = 156 + 0.8 = 156.8, new total = (n + 5) × 156.8. Equation: 156n + 800 = 156.8(n + 5). Solving: 156n + 800 = 156.8n + 784. So 800 - 784 = 156.8n - 156.8, giving 16 = 0.8n, thus n = 20. Initially there were 20 students.