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

Answer is 35

Let age of newly appointed teacher is N

⇒ 1000 - 60 + N = 975

⇒ N = 35 years

Answer 2

Let x=Sum of ages of teachers

Mean=x/25

40=x/25

x=40×25

=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 

=39×25

=975

 ....

∵the mean=39

Now, 

975−940 = Age of new teacher

Therefore, age of new teacher is 

35years.