The average age of 20 students and a class teacher is 30 years. If class teacher's age is excluded, the average age is reduced by 1 year. What is the class teacher's age?

Total age of 21 people (20 students + 1 teacher) = 21 × 30 = 630 years. When teacher's age is excluded, average of 20 students = 29 years, so their total = 20 × 29 = 580 years. Teacher's age = Total - Students' total = 630 - 580 = 50 years. Alternatively: removing the teacher reduces average by 1, so teacher's age = new average + original number of people = 29 + 21 = 50.