Step 1: Understanding the Question:
This is an average-based problem. We must determine the teacher's weight using the students' initial average and the updated average after the teacher is added.
Step 2: Key Formula or Approach:
The average is computed as:
\[ \text{Average} = \frac{\text{Sum of all values}}{\text{Total number of values}} \]
The teacher's weight equals the new total weight minus the original total weight of the students.
Step 3: Detailed Explanation:
The starting average for 30 students is 40 kg.
\[ \text{Total weight of 30 students} = 30 \times 40 = 1200 \text{ kg} \]
Including the teacher raises the total count to \(30 + 1 = 31\) people.
The average rises by 1 kg, making the new average \(40 + 1 = 41\) kg.
\[ \text{Total weight of 31 individuals} = 31 \times 41 \]
\[ 31 \times 41 = 1271 \text{ kg} \]
Subtracting the initial total from the new total gives the teacher's weight:
\[ \text{Weight of teacher} = 1271 - 1200 = 71 \text{ kg} \]
Step 4: Final Answer:
The correct choice is (B).