Question

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 ______.

Options

• 32

• 33

• 34

• 35

Answer 1

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 35.

Explanation:

Let x₁, x₂, ....., x₂₅ be teachers.

Since, the mean age of 25 teachers is 40.

Then, x₁ + x₂ + ..... + x₂₅ = 25 × 40  ...(i)

Let the age of new teacher is A.

Then (x₁ + x₂ + ..... + x₂₅) – 60 + A = 25 × 39

⇒ A = 975 + 60 – 1000 = 35 years

Hence, the age of newly appointed teacher is 35 years.