The average age of 59 students of a class is 22 years. If the age of the teacher is also included, the average age of the whole group becomes 23 years. The age (in years) of the teacher is:

Correct option is D

Given:

The average age of 59 students = 22 years

The average age of the whole group (59 students + 1 teacher) = 23 years

Formula Used:

Total age of the group = Average age of the group × Number of people in the group

Solution:

Total age of 59 students: = 22 × 59 = 1298 years

Total age of 60 people (59 students + teacher) = 23 × 60 = 1380 years

Teacher’s age = 1380 – 1298 = 82 years

Thus, the age of the teacher is 82 years.

Alternate Solution: 

If the teacher age is included the increase in the age = 23 - 22 = 1 year 

total increase =  $$1\times 60$$ = 60 year 

So, the teacher age = 22 + 60 = 82 year