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. Then the age of new teacher is:

• A. $28$ years
• B. $25$ years
• C. $20$ years
• D. $18$ years

Answer 1

The correct option is C $20$ years

Let the average age of the staff $=x$.

and age of the new teacher $=y$.

According to the question,

Average age of the staff reduced by $2$ years.

$\Rightarrow \frac{20x-60+y}{20}=x-2$

$\Rightarrow 20x-60+y=20(x-2)$

$\Rightarrow 20x-60+y=20x-40$

$\Rightarrow y=60-40=20$.

Hence, the age of the new teacher is $20$ years.

Therefore, option $C$ is correct.