Question

The mean age of a class is 16 years . If the class teacher aged 40 years old is also included, the mean age increases to 17 years. The number of students in the class are:

(a) 23
(b) 33
(c) 44
(d) 16

Answer 1

let the total number of students in a class be x
total age of all students=16x
when the teacher is added, number of person=x+1
so, 17x+17=16x+40
x=23

Answer 2

Given:

The mean age of a class is 16 years .

If the class teacher aged 40 years old is also included, the mean age increases to 17 years.

To Find:

The number of students in the class are:

Solution:

Let x be the number of students in class

The mean age of a class is 16 years .

$Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}$

$16=\frac{\text{Sum of ages of x students}}{x}$

$16x=\text{Sum of ages of x students}$

If the class teacher aged 40 years old is also included, the mean age increases to 17 years.

New sum = 16x+40

New mean = 17

So,$17=\frac{16x+40}{x+1}$

17x+17=16x+40

x=23

Hence The number of students in the class are 23