Question

The average weight of a class of 30 students is 40 kg. If the teacher's weight is included, the average increases by 1 kg. What is the weight of the teacher?

• A. 70 kg
• B. 71 kg
• C. 72 kg
• D. 75 kg

Hint:

Shortcut: Age/Weight of the new person = Old Average + (Total new members \(\times\) Increase in Average). Here, \(40 + (31 \times 1) = 71\) kg.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question deals with averages. We need to calculate the weight of the teacher given the initial average weight of the students and the new average when the teacher is included.


Step 2: Key Formula or Approach:
The formula for calculating an average is:
\[ \text{Average} = \frac{\text{Sum of all values}}{\text{Total number of values}} \] The weight of the teacher can be found by taking the difference between the total weight including the teacher and the initial total weight of the students.


Step 3: Detailed Explanation:
The initial average weight of 30 students is 40 kg.
\[ \text{Total weight of 30 students} = 30 \times 40 = 1200 \text{ kg} \] When the teacher is included, the total number of individuals becomes \(30 + 1 = 31\).
The new average weight increases by 1 kg, so it becomes \(40 + 1 = 41\) kg.
\[ \text{Total weight of 31 individuals} = 31 \times 41 \] \[ 31 \times 41 = 1271 \text{ kg} \] The weight of the teacher is the difference between the two total weights:
\[ \text{Weight of teacher} = 1271 - 1200 = 71 \text{ kg} \]

Step 4: Final Answer:
The correct choice is (B).