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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 20
Given :
Average height of some students = 156 cm
Average height of 5 students = 160 cm
Formula used :
Average = Sum of observation/number of observations ---- (1)
Calculations :
Let the number of students be x
Sum of height of x students = 156x ---- (1)
Sum of height of 5 students = 5 × 160 = 800 cm ---- (2)
New average = 156 + 0.8 = 156.8 cm
Total number of new students = x + 5
Sum of (x + 5) students = (x + 5) × 156.8
⇒ 156.8x + 784 ---- (3)
Equating equation (1) + (2) and (3)
⇒ 800 + 156x = 156.8x + 784
⇒ 16 = 0.8x
⇒ x = 20
Hence, total number of students = 20