The average age of 48 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 B

Given:

The average age of 48 students = 22 years

The average age of the whole group (48 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 48 students: = 22 × 48 = 1056 years

Total age of 49 people (48 students + teacher) = 23 × 49 = 1127 years

Teacher’s age = 1127 – 1056 = 71 years

Thus, the age of the teacher is 71 years.

Alternate Solution: 

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

total increase =  $$1\times 49$$​ = 49 year 

So, the teacher age = 22 + 49 = 71 year