The average weight of 21 boys is 64 kg. When the teacher is included (22 people), the average increases by 1 kg. What is the teacher's weight?

Introduction / Context:
Adding one person and seeing the mean increase by a fixed amount allows us to compute the added person's value from new total minus old total. This is a standard trick in averages.

Given Data / Assumptions:

• 21 boys; mean = 64 kg.
• With teacher: 22 people; mean = 65 kg.
• Find teacher's weight.

Concept / Approach:
Totals method: teacher's weight = (new mean * new count) − (old mean * old count).

Step-by-Step Solution:

Verification / Alternative check:
Plug back: (1344 + 86) / 22 = 1430 / 22 = 65, confirming the +1 kg increase in the average.

Why Other Options Are Wrong:
64kg, 72 kg, 98 kg: Do not satisfy the totals calculation; 64 kg would not increase the mean at all.

Common Pitfalls:
Adding 1 kg directly to 64 for the teacher (incorrect), rather than computing via totals.

Final Answer:
86kg