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Question 86

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 ________.


Correct Answer: 35

Solution

The mean age of 25 teachers is 40 years, so the total age of all 25 teachers is $$25 \times 40 = 1000$$ years.

A teacher aged 60 retires and is replaced by a new teacher of age $$x$$. The new total age becomes $$1000 - 60 + x = 940 + x$$.

The new mean age is 39, and there are still 25 teachers, so $$\frac{940 + x}{25} = 39$$.

Solving: $$940 + x = 25 \times 39 = 975$$, so $$x = 975 - 940 = 35$$.

Therefore, the age of the newly appointed teacher is $$35$$ years.

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