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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

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answer is B.

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Detailed Solution

Mean age of $25$ teachers in a school $= 40$ years

$\Rightarrow \frac{x_{1} + x_{2} + \dots + x_{25}}{25} = 40$

$\Rightarrow x_{1} + x_{2} + \dots . + x_{25} = 1000$

Let $A$ be the age of new teacher. Then according to

question, we have

$x_{1} + x_{2}$ $+ \dots \dots + x_{25} - 60 + A =$ New mean $x 25$

$\Rightarrow$ $1000 - 60 + A = 39 \times 25 = 975$

$\Rightarrow$ $A = 975 - 940 = 35$

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