The average weight of some members of a club is 70 kg. If 15 members with an average weight of 60 kg join the club, or if 5 members with an average weight of 90 kg leave the club, then the average weight of members in both cases is equal. How many members were there in the club initially?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 45.
Let the initial number of members = n
(70n + 15 × 60)/(n + 15) = (70n - 5 × 90)/(n - 5)
⇒ (70n + 900)/(n + 15) = (70n - 450)/(n - 5)
⇒ 70n² - 350n + 900n - 4500 = 70n² + 1050n - 450n - 6750
⇒ 550n - 4500 = 600n - 6750
⇒ -50n = -2250
⇒ n = 45