Question

A school has 20 teachers. One of them retires at the age of 60 years and a new teacher replaces him. This change reduces the average age of the staff by 2 years. Find the age of new teacher
A. 28
B. 25
C. 20
D. 18

Answer 1

Hint:We start solving the problem by assuming the average age of the 20 teachers. So, we get a new average. From these two averages, we find two total age of before and after the change. The difference between these two totals is the solution of the problem.

Complete step by step answer:
Let’s assume the average of the 20 teachers before one teacher retires is x years.
So, the average of 20 teachers is x.
The total age of them is $\left( 20\times x \right)=20x$ years.
After the teacher retired the change reduced the average age of the staff by 2 years.
So, the average becomes $\left( x-2 \right)$ years.
After the new teacher arrived the total number of teachers is still 20.
The total age is $20\times \left( x-2 \right)=20\left( x-2 \right)$ years.
The change of these two totals is the reduced age value from the age of the retired teacher.
So, the difference is \[20x-20\left( x-2 \right)=20x-20x+40=40\].
The age of the retired teacher is 60 years.
The age of the new teacher is 40 years less.
So, the age of the new teacher is $60-40=20$ years.
The correct option is (C).

Note:
 We can also solve the problem by only looking at the change in average. As the average reduced, it means the new teacher is younger. The total age change is $20\times 2=40$ years. So, the age of the new teacher is $60-40=20$ years. In that case, we don’t need to use the variable.