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 new teacher

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

Answer 1

Answer: (C)

20 years

Let the initial average of $20$ teachers be $x$

Then sum of age of $20$ teachers $=20x$

One teacher gets retired

Now age of $19$ teachers $=20x-60$

Let the age of new teacher be $y$

Now age of $20$ teachers $=20x-60+y$

New average is $2$ less than the previous average

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

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

$\therefore$ $y=20$

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