The average age of 30 boys in a class is 10 years. If the age of their teacher is also included, the average age of all of them increases by 1 year. What is the teacher's present age (in years)?

Introduction / Context:
This question involves average age and the effect of adding one more person (the teacher) to the group. We know the average age of 30 boys and the new average when the teacher is included. From this information, we must calculate the teacher's present age. This is a standard problem type in aptitude tests on averages and ages.

Given Data / Assumptions:

- There are 30 boys in the class.
- The average age of these 30 boys is 10 years.
- When the teacher's age is included, there are 31 persons, and the average age becomes 11 years.
- We are asked to find the teacher's present age.

Concept / Approach:
Average age is total age divided by number of people. We can first calculate the total age of the 30 boys from their average. Then we calculate the total age of the 30 boys plus the teacher from the new average. The difference between these two totals gives the teacher's age. This uses the formula total age = average age × number of persons.

Step-by-Step Solution:
Step 1: Total age of the 30 boys = 30 × 10 = 300 years. Step 2: When the teacher is included, the total number of persons is 31. Step 3: The new average age is 11 years. Step 4: Total age of the 30 boys plus the teacher = 31 × 11 = 341 years. Step 5: Let the teacher's age be T years. Then 300 + T = 341. Step 6: Solve for T: T = 341 − 300 = 41 years.

Verification / Alternative check:
If the teacher is 41 years old, then the total age of all 31 persons is 300 + 41 = 341 years. Dividing this by 31 gives an average age of 11 years, which matches the condition in the question. Therefore, the calculation is consistent and confirms that the teacher's age is 41 years.

Why Other Options Are Wrong:
If the teacher were 30, 38, 40 or 45 years old, the total age of the group would be 330, 338, 340 or 345 years respectively, and the corresponding averages for 31 persons would not equal 11 years. Only 41 years gives the correct new average.

Common Pitfalls:
Students sometimes treat 11 years as the teacher's age or mistakenly average the numbers 10 and 11. Others may forget to change the count of persons from 30 to 31 when including the teacher. Always remember to convert averages to totals before adding or subtracting ages in such problems.

Final Answer:
The teacher's present age is 41 years.