The average age of a class of 39 students is 15 years. If the age of the teacher is included, the average increases by 3 months. What is the age of the teacher in years?

Introduction / Context:
This question tests your understanding of averages, especially when a new member is added to a group. The class has 39 students with a known average age, and when the teacher is added, the average increases slightly by 3 months. From this new average, you must compute the teacher age. This type of problem appears frequently in competitive exams because it requires comfortable handling of both averages and small unit conversions, such as months to years.

Given Data / Assumptions:

• The class has 39 students with an average age of 15 years.
• When the teacher is added, the average age increases by 3 months.
• 3 months is one quarter of a year, that is 0.25 years.
• The new average age with the teacher included is therefore 15.25 years.
• We must find the teacher age.

Concept / Approach:
Average age is total age divided by number of individuals. First, calculate the total age of all 39 students. Then, calculate the total age for 40 individuals (39 students plus the teacher) using the new average. The difference between these two totals gives the teacher age. This approach is systematic and avoids confusion about how the additional person affects the average.

Step-by-Step Solution:
Step 1: Compute the total age of 39 students as 39 × 15 = 585 years. Step 2: When the teacher is included, the group becomes 40 individuals with an average age of 15.25 years. Step 3: Compute the total age of these 40 individuals as 40 × 15.25 = 610 years. Step 4: The teacher age is the difference between the total age with the teacher and the total age of the students alone, so teacher age = 610 − 585 = 25 years. Step 5: Thus, the teacher age is 25 years.

Verification / Alternative check:
Think in terms of the effect of the teacher age compared to the original average. The new average is higher by 0.25 years across 40 individuals, which means the total increase in age is 40 × 0.25 = 10 years. Therefore, the teacher must be 10 years older than the original average, so the teacher age is 15 + 10 = 25 years. This matches the previous calculation using totals and confirms that the answer is correct.

Why Other Options Are Wrong:
Option 30: This would produce a larger increase in total age than necessary and result in an average more than 15.25 years.
Option 35 and 40: These values are much higher than required to increase the average by only 3 months and would give a larger jump in the group average.
Option 28: Although closer, it still yields a larger total than the allowed 610 years and does not correspond to the given new average.

Common Pitfalls:
A frequent mistake is to treat 3 months as 3 years or 0.3 years, which leads to incorrect totals. Another error is to forget that the number of individuals changes from 39 to 40 when the teacher is added. Always convert months to years correctly and remember that total age equals average multiplied by number of people. Verifying the result by checking the implied average is a good way to catch mistakes.

Final Answer:
The age of the teacher is 25 years.