The average age of 26 students in a class is 15 years. If teacher's age is included in it, then the average will increase by one. What is the teacher's age (in years)?
- A38
- B40
- C42
- D33
Solution & Step-by-step Explanation
Method 1: Total Sum Method
Total age of 26 students:
Sum
26
=26×15=390 years
When the teacher's age is included, the total number of people becomes 27 and the average increases by 1 (i.e., 15+1=16 years).
Total age of 27 people:
Sum
27
=27×16=432 years
Teacher's age:
Teacher’s age=Sum
27
−Sum
26
=432−390=42 years
Method 2: Deviation Method
Teacher’s age=New Average+(Initial number of people×Increase in average)
Teacher’s age=16+(26×1)=16+26=42 years
Total age of 26 students:
Sum
26
=26×15=390 years
When the teacher's age is included, the total number of people becomes 27 and the average increases by 1 (i.e., 15+1=16 years).
Total age of 27 people:
Sum
27
=27×16=432 years
Teacher's age:
Teacher’s age=Sum
27
−Sum
26
=432−390=42 years
Method 2: Deviation Method
Teacher’s age=New Average+(Initial number of people×Increase in average)
Teacher’s age=16+(26×1)=16+26=42 years