Out of 10 teachers of a school, one teacher retires and in his place a new teacher of age 25 years joins. As a result of it, the average age of the teachers is reduced by 3 years. The age of the retired teacher is

Let original average age = A. Total age of 10 teachers = 10A. After replacement: new teacher age = 25, new average = A - 3. New total age = 10(A - 3) = 10A - 30. Change in total age = (10A - 30) - 10A = -30. This equals new teacher age - retired teacher age = 25 - R. So 25 - R = -30, R = 55. The retired teacher was 55 years old.