Question:

The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?

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A faster method: The teacher's age must be the new average plus the total increase given to the rest of the group. \(\text{Teacher's age} = \text{New Average} + (\text{Number of students} \times \text{Increase}) = 22 + (22 \times 1) = 44\).
Updated On: May 9, 2026
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The Correct Option is D

Solution and Explanation



Step 1: Understanding the Question:

We need to find the age of the teacher based on the change in the average age of a group when the teacher is added to it.


Step 2: Key Formula or Approach:

The sum of all ages equals the average age multiplied by the number of people.
\(\text{Sum} = \text{Average} \times N\).
The age of the newly added person is the difference between the new sum and the old sum.


Step 3: Detailed Explanation:

First, calculate the total age of the \(22\) students. \[ \text{Total age of students} = 22 \times 21 = 462 \text{ years} \] When the teacher is included, the total number of people becomes \(22 + 1 = 23\).
The new average age increases by \(1\), so it becomes \(21 + 1 = 22\) years.
Now, calculate the new total age of the students and the teacher combined. \[ \text{New total age} = 23 \times 22 = 506 \text{ years} \] The age of the teacher is the difference between the new total age and the original total age. \[ \text{Age of teacher} = 506 - 462 = 44 \text{ years} \]

Step 4: Final Answer:

The age of the teacher is \(44\) years.
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