The average weight of a class of 24 students is 35 kg. When the weight of the teacher is also included, the average weight increases by 400 grams (0.4 kg). What is the weight, in kilograms, of the teacher?

Introduction / Context:
This question focuses on how the average (mean) changes when an additional data point (the teacher's weight) is added to a group. We use the relationship between total weight, number of persons, and average to determine the teacher's weight. Converting 400 grams into kilograms is an important small detail here.

Given Data / Assumptions:

• Number of students = 24.
• Average weight of students = 35 kg.
• Teacher's weight is added to form a group of 25 people.
• New average weight = 35 kg + 0.4 kg = 35.4 kg.
• We need to find the teacher's weight in kg.

Concept / Approach:
Average (mean) is: average = total weight / number of persons. We first compute the total weight of the 24 students. Then we compute the total weight of all 25 persons using the new average. The difference between these totals directly gives the teacher's weight.

Step-by-Step Solution:
Step 1: Total weight of 24 students = 24 * 35 kg. 24 * 35 = 840, so total = 840 kg. Step 2: New average after including teacher = 35.4 kg. Number of persons now = 24 + 1 = 25. Step 3: Total weight of 25 persons = 25 * 35.4 kg. Compute 25 * 35.4 = (25 * 35) + (25 * 0.4) = 875 + 10 = 885 kg. Step 4: Teacher's weight = total weight of 25 persons - total weight of 24 students. Teacher's weight = 885 - 840 = 45 kg.
Verification / Alternative check:
If we add a 45 kg teacher to the 24 students whose total is 840 kg, new total = 840 + 45 = 885 kg. New average = 885 / 25 = 35.4 kg, which matches the required average (35 kg + 0.4 kg).
Why Other Options Are Wrong:
Weights 46 kg, 47 kg, 48 kg, or 50 kg would produce totals different from 885 kg, and so the average would not be 35.4 kg. For example, if the teacher weighed 48 kg, total = 840 + 48 = 888 kg and average = 888 / 25 = 35.52 kg, which is too high.
Common Pitfalls:
Students sometimes forget to convert 400 g to 0.4 kg and may mistakenly add 400 to 35. Another mistake is using 24 instead of 25 when multiplying the new average, which gives the wrong total.
Final Answer:
The weight of the teacher is 45 kg.