The average age of 20 students of a class is 27 years. If the age of the…
2025
The average age of 20 students of a class is 27 years. If the age of the teacher is also included, the average age of the whole group becomes 28 years. The age (in years) of the teacher is:
- A.
48
- B.
47
- C.
45
- D.
51
Attempted by 12 students.
Show answer & explanation
Correct answer: A
Concept
When one new member joins a group of n original members whose average is a₁, and the average of all (n + 1) members becomes a₂, the new member’s value can be found from the change in total: New value = (n + 1) × a₂ − n × a₁, since total = average × count.
Application
Total age of the 20 students = 20 × 27 = 540 years.
Total age of all 21 people (20 students + teacher) = 21 × 28 = 588 years.
Teacher’s age = total with teacher − total without teacher = 588 − 540 = 48 years.
Cross-check
Adding 48 to the students’ total gives (540 + 48) ÷ 21 = 588 ÷ 21 = 28, which matches the stated new average, confirming the result. The teacher’s age is 48 years.