The average weight of a class of 24 students is 35 kg. When the teacher is included, the average becomes 35.4 kg (an increase of 400 g). What is the weight of the teacher?

Introduction / Context:
This problem involves the concept of average weight when an additional person is added to a group. We are given the average weight of 24 students and the new average when the teacher joins them. From this information, we must determine the teacher weight. This type of question trains students to work comfortably with averages and total sums.

Given Data / Assumptions:
- Number of students = 24.
- Average weight of students alone = 35 kg.
- When the teacher is included, total persons = 25.
- New average weight = 35.4 kg (which is 35 kg + 0.4 kg, that is 400 g increase).
- We need to find the teacher weight in kilograms.

Concept / Approach:
The idea is that average multiplied by number of persons gives the total weight. We first compute the total weight of the 24 students. Then we compute the total combined weight of 24 students plus teacher using the new average. The difference between these two totals must be exactly the teacher weight. This is a direct application of average = total sum / number of terms.

Step-by-Step Solution:
Step 1: Total weight of the 24 students = 24 * 35 = 840 kg.Step 2: After adding the teacher, the number of persons is 25 and the new average is 35.4 kg.Step 3: Total weight of 24 students plus teacher = 25 * 35.4.Step 4: Compute this total: 25 * 35.4 = 885 kg.Step 5: Teacher weight = combined total weight minus weight of students = 885 - 840 = 45 kg.

Verification / Alternative Check:
We can confirm by checking the new average. If the teacher weighs 45 kg, the total weight is 840 + 45 = 885 kg for 25 persons. The average is then 885 / 25 = 35.4 kg, which matches the given new average. This confirms that 45 kg is correct.

Why Other Options Are Wrong:
If the teacher weighed 46 kg, the total would be 886 kg and the average would be 886 / 25 = 35.44 kg, not 35.4 kg. For 47 kg, the average would be even higher, and for 48 kg the deviation is larger. Any weight other than 45 kg fails to give the exact new average of 35.4 kg specified in the question statement.

Common Pitfalls:
A common error is to add 0.4 kg directly to 35 kg and assume that the teacher weight is 35.4 kg, which is incorrect because that value is an average, not an individual weight. Another mistake is to forget to change the number of persons from 24 to 25 after including the teacher. Students should always translate averages into total sums and then work backward to find missing values.

Final Answer:
The weight of the teacher is 45 kg.