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 now the mean age of the teachers in this school is $39$ years, then the age (in years) of the newly appointed teacher is:

• A. $40$
• B. $30$
• C. $25$
• D. $35$

Answer 1

Answer: (D)

$35$

Let $x=$Sum of ages of teachers
Mean$=\frac{x}{25}$
$\Rightarrow 40=\frac{x}{25}$
$\Rightarrow x=40\times 25$
$\Rightarrow x=1000$
A new teacher appointed in place of a teacher whose age is $60$.
So, Sum of ages of remaining 24 teachers $=x-60=1000-60=940$.
The sum of ages of all 25 teachers including new teacher $=39\times 25=975$ ....$\because \text{the mean}=39$
Now, $975-940=$ Age of new teacher
Therefore, age of new teacher is $35$ years.