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:

Let x = Sum of ages of teachers
Mean = x/25 ⇒ 40 = x/25 ⇒ x = 40 × 25 ⇒ 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 the new teacher = 39 × 25 = 975 (since the mean = 39)
Now, 975 - 940 = Age of new teacher
Therefore, the age of the new teacher is 35 years.