The average age of 14 students and their teacher is 20 years. If the teacher is excluded, then their average age reduces by 1.5 years. The teacher’s age is:

Correct option is A

Given:
The average age of 14 students + 1 teacher = 20 years
The average age of 14 students (excluding the teacher) = (20 - 1.5) = 18.5 years

Formula Used:
Total Age =Average Age × Number of People

Solution:

​14 students + 1 teacher = 15  persons

Sum of ages of 15 persons = $$15 \times 20 = 300 \text{ years}$$​​

When teacher is excluded, sum of ages of remaining 14 persons :

= $$14 \times (20 - 1.5) = 259 \text{ years}$$​​

Teacher's age = 300 - 259 = 41 years