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 __________.

Hint:

New Mean = Old Mean + $\frac{\text{Change in total value}}{N}$. Here, $39 = 40 + \frac{x-60}{25}$.

Answer 1

Correct Answer: 35

Step 1: Total age of 25 teachers $= 25 \times 40 = 1000$ years.
Step 2: New total age after retirement and new appointment $= 25 \times 39 = 975$ years.
Step 3: Change in total age $= 975 - 1000 = -25$ years.
Step 4: Let new teacher's age be $x$. $x - 60 = -25$.
Step 5: $x = 60 - 25 = 35$ years.