-  Avg x Number = Total
30 nos x 21 years = 630 years                   …..(1)
30 nos x 22 years = 682 years                   …..(2)
Teacher's age = (2) - (1) = 682 - 630 = 52 years.

Average is the sum of all the values divided by the number of values.

Therefore, the average of the 30 students (without the teacher) = 21

Let 'x' be the teacher's age.

Therefore, the average of the 30 students (including the teacher) = 21 + 1 = 22

Formula for Average:
Average = Sum of all values/ Number of values

Therefore,
22 = (30×21 + x)/31

On solving the above equation,
x = 31×22 - 30×21
= 682 - 630
= 52

Hence, the teacher's age is 52 years.

Therefore, the correct option is option D: 52 years.