Question

The mean age of $25$ teachers in a school is $40$ years. A teacher retires at the age of $60$ years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is $39$ years, then the age (in years) of the newly appointed teacher is

Answer 1

Compute the age of the newly appointed teacher.

Assume that the ages of $25$ teachers are as follows: $x_1,x_2,x_3,.......x_{25}$.

It is given that the mean age of $25$ teachers is $40$ years.

Therefore, $\frac{x_1+x_2+x_3+.......+x_{25}}{25}=40...1$

Since a teacher retires at the age of $60$ years and a teacher joined and the new mean age is $39$.

Assume that, the age of the newly joined teacher is $a$.

Therefore,

$$\begin{gathered} \frac{x_1+x_2+x_3+.......+x_{25}-60+a}{25}=39 \\ \Rightarrow \frac{x_1+x_2+x_3+.......+x_{25}}{25}+\frac{-60+a}{25}=39...2 \end{gathered}$$

From equation $1$ and equation $2$.

$$\begin{gathered} 40+\frac{-60+a}{25}=39 \\ \Rightarrow \frac{-60+a}{25}=-1 \\ \Rightarrow -60+a=-25 \\ \Rightarrow a=35 \end{gathered}$$

Therefore, the age of the newly appointed teacher is $35$ years.