The average age of eight teachers in a school is 40 years. One teacher among them dies at the age of 55 years and another teacher whose age is 39 years joins the staff. What is the new average age in years of the teachers in the school now?

Introduction / Context:
This problem combines the concept of average with a change in the group membership. One teacher leaves (by death) and another teacher joins with a different age. You are asked to find the new average age of the group. Such questions are common in aptitude tests and are useful practice for understanding how averages are affected when one value is removed and another is added.

Given Data / Assumptions:

• There are eight teachers initially.
• The average age of these eight teachers is 40 years.
• One teacher dies at the age of 55 years.
• A new teacher aged 39 years joins the group.
• The number of teachers after the change remains eight.
• We must find the new average age of the teachers.

Concept / Approach:
Average age is the total of all ages divided by the number of people. Initially, we can find the total age of the eight teachers by multiplying the average by the number of teachers. When one teacher leaves, we subtract that age from the total. When a new teacher joins, we add the new age. The number of teachers remains the same, so the new average is the adjusted total divided by the same number of teachers. This method is simpler and more reliable than trying to track each individual age.

Step-by-Step Solution:
Step 1: Compute the initial total age of the eight teachers as 8 × 40 = 320 years. Step 2: One teacher aged 55 leaves, so subtract 55 from 320 to get 265 years as the total age of the remaining seven teachers. Step 3: A new teacher aged 39 joins, so add 39 to 265 to get a new total of 304 years. Step 4: There are still eight teachers in the group, so the new average age is 304 ÷ 8 = 38 years. Step 5: Thus the new average age of the teachers is 38 years.

Verification / Alternative check:
We can also reason about the change in average without computing every detail. The teacher who left was 55 years old, which is 15 years above the original average of 40. The teacher who joined is 39 years old, which is 1 year below 40. Effectively, we removed an age that was 15 above the old average and added an age that is 1 below it, a net change of 16 years less in total over 8 people. A decrease of 16 in total divided by 8 teachers gives a decrease of 2 in the average, moving it from 40 down to 38, which matches our calculation.

Why Other Options Are Wrong:
Option 35 and 36: These would require a larger drop in the total age than what actually occurs when 55 is replaced by 39.
Option 39: This would imply almost no significant effect from replacing a 55 year old teacher with a 39 year old one, which is not correct.
Option 40: This is the original average and does not reflect the change in the staff composition.

Common Pitfalls:
A common mistake is to forget that the number of teachers stays the same after one leaves and another joins, leading to an incorrect divisor when calculating the new average. Another error is to add and subtract the ages incorrectly, especially when doing mental arithmetic. Writing down each step clearly and double checking the computed totals will help avoid such calculation errors.

Final Answer:
The new average age of the teachers is 38 years.