-  Avg x Number = Total
27 nos x 20 years = 400                  ….(1)
21 nos x 21 years = 441                  ….(2)
Teacher's age = (2) - (1) = 441 - 400 = 41 years.

The average age of a group of people can be calculated by dividing the sum of their ages by the number of people in the group. If the average age of a class of 20 students is 20 years, it means that the sum of the ages of all 20 students is 20 years x 20 students = 400 years.

When the teacher's age is added to the group, the number of people in the group increases to 21. The average age of the group then increases to 21 years, which is 1 year more than the average age of the students before the teacher's age was added. This means that the sum of the ages of all 21 people is now 21 years x 21 people = 441 years.

We can use the information that the sum of the ages of the students is 400 years and the sum of the ages of all 21 people is 441 years to find the teacher's age.

Let's call the teacher's age "x". The equation for the sum of the ages of all 21 people is:

x + 400 = 441

Solving for x, we find that:

x = 41

So, the teacher's age is 41 years.

Explanation with bullet points:

• The average age of 20 students is 20 years.
• The sum of the ages of all 20 students is 20 x 20 = 400 years.
• When the teacher's age is added to the group, the average age of the group increases to 21 years.
• The sum of the ages of all 21 people is 21 x 21 = 441 years.
• Using the information that the sum of the ages of the students is 400 years and the sum of the ages of all 21 people is 441 years, we can find the teacher's age.
• Letting the teacher's age be "x", the equation for the sum of the ages of all 21 people is: x + 400 = 441
• Solving for x, we find that x = 41.
• So, the teacher's age is 41 years.

Hence, the correct answer is C.