The average age of 22 students of a class is 11 years. If the age of the…
2025
The average age of 22 students of a class is 11 years. If the age of the teacher is also included, the average age of the whole group becomes 12 years. The age (in years) of the teacher is:
- A.
34
- B.
35
- C.
37
- D.
38
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: Average = Sum of values ÷ Number of values, so Sum of values = Average × Number of values. When one more member joins a group, the new sum equals the new average multiplied by the new total count, and the joining member's own value equals the new sum minus the old sum.
Sum of ages of the 22 students = 22 × 11 = 242 years.
After the teacher joins, total people = 23 and the new average = 12 years, so the new sum of ages = 23 × 12 = 276 years.
Teacher's age = New sum − Old sum = 276 − 242 = 34 years.
Cross-check: Adding the teacher's age of 34 years back to the students' total: (242 + 34) ÷ 23 = 276 ÷ 23 = 12 years, which matches the given new average, confirming the result.
Hence, the teacher's age is 34 years.