15 years ago, the average age of all the 40 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 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?

Solution

15 years ago, Average age of 40 teachers = 50 years 8 years ago (just before retirement of Principal), Average age of 40 teachers = 50 + 7 = 57 years And the same time total age of 40 teachers = 40 × 57 = 2280 years And the total age of remaining 39 teachers when just the principal has retired = 2280 – 60 = 2220 years 1 year later (i.e, 7 years ago from present) Total age of 39 teachers (just before the recruitment of new Principal) = 2220 + (1 × 39) = 2259 years And the total age of 40 teachers including new principal just after the recruitment = 2259 + 56 = 2315 years Thus, the present age of all 40 Teachers = 2315 + (7 × 40) = 2595 years ∴ Present average age of all the 40 Teachers = 2595/40 = 519/8 years.