15 years ago, the average age of all the 80 teachers of the college was 50 years. 8 years ago, the principal has retired from her post at the age of 60 years. So after one year from that a new principal whose age was 56 years recruited from outside. Find the present average age of all the teachers is, if principal is also considered as a teacher?

15 years ago, Average age of 80 teachers = 50 years 8 years ago (just before retirement of Principal), Average age of 80 teachers = 50 + 7 = 57 years And the same time total age of 80 teachers = 80 × 57 = 4560 years And the total age of remaining 79 teachers when just the principal has retired = 4560 – 60 = 4500 years 1 year later (i.e, 7 years ago from present) Total age of 79 teachers (just before the recruitment of new Principal) = 4500 + (1 × 79) = 4579 years And the total age of 80 teachers including new principal just after the recruitment = 4579 + 56 = 4635 years Thus, the present age of all 80 Teachers = 4635 + (7 × 80) = 5195 years ∴ Present average age of all the 80 Teachers = 5195/80 years. Alternate method: Let the present average age of all teachers be X The sum of the age of all the teachers 15 years ago = 80 × 50 = 4000 years 8 years ago the sum of the age of the teachers = 4000 + (7 × 80) - 60 = 4000 + 560 - 60 = 4500 years When new principle is recruited then age of the teachers = 4500 + (79 × 1) + 56 = 4500 + 79 + 56 = 4635 years The sum of the age of the teachers at present = 4635 + (7 × 80) = 4635 + 560 = 5195 years The present average age of all the teachers = 5195/80