The average weight of some boys in a group is 45 kg. If 10 boys with an average weight of 39 kg join the group or 10 boys with an average weight of 49 kg leave the group, then the average weight of boys in both cases is equal. How many boys were there in the group initially?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 50.
Let the initial number of boys = N
(45N + 390)/(N + 10) = (45N - 490)/(N - 10)
⇒ 45N2 - 450N + 390N - 3900 = 45N2 + 450N - 490N - 4900
⇒ -60N - 3900 = -40N - 4900
⇒ -20N = -1000
⇒ N = 50