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

$x_1+x_2+\cdots +x_{25}=25\times 40=1000$
$\Rightarrow \frac{x_1+x_2+\cdots +x_{25}-60+a}{25}=39$
$\Rightarrow 100-60+a=25\times 39$
$\Rightarrow a=-940+975$
$\Rightarrow a=35$