The average age of a class of 29 students is 20 years. If the age of the teacher is included, then the average increases by 3 months. Find the age of the teacher.

Average = Sum of Quantities/Number of Quantities

1) First calculate the total age of 40 students
Total age of 29 students = ( Average age x No. of students)
= (20 x 29) = 580 years

2) Average age of 29 students + 1 teacher = 20 years + 3 months = 81/4 years

3) Finally the total age of 29 students + 1 teacher = 81/4 × 30 = 607.5 years

Therefore, age of teacher = (Total age of 30 members - Total age of 29 students)
= (607.5 – 580)
= 27.5 years.