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Q.

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

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answer is 35.

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Detailed Solution

$x_{1}, x_{2}, x_{3}, \dots \dots \dots x_{25}$ be teachers Mean= 40
$\Rightarrow \frac{x_{1} + x_{2} + x_{3} \dots \dots \dots + x_{25,}}{25} = 40$
$\Rightarrow \sum_{i = 1}^{25} x_{i,} = 1000$
Let the age of new teacher is A Mean is 39
$\Rightarrow \frac{\sum_{i = 1}^{25} x_{i,} - 60 + A}{25} = 39$
$\Rightarrow 1000 - 60 + A = 25 \times 39 = 975 \Rightarrow A = 975 + 60 - 1000 = 35 YEARS$

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