Out of 8 lecturers of a college, one lecturer retires and at his place a new lecturer of age 32 years joins. As a result, the average age of lecturers is reduced by 4 years. The age of the retired lecturer is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 64 years.
Let the average age of 8 lecturers before retirement = A
Then total age = 8A
After retirement, one leaves and a new lecturer of 32 joins → new average = A − 4
So total new age = 8(A − 4) = 8A − 32
But also total new age = (8A − age of retired lecturer) + 32
So:
8A − age + 32 = 8A − 32
⇒ −age + 32 = −32 ⇒ age = 64