Question Number 104972 by 1549442205PVT last updated on 25/Jul/20

  In the a  sport camp, 65% children know  playing the football,70%−in voleyball,75%−in  basketball.What is least number of children who  know playing all above three sport games?  (Answer 10%)

Answered by mr W last updated on 25/Jul/20

simple way without using set theory:    N_F =children playing football only  N_(F,V) =children playing both football and volleyball  N_(F,V,B) =children playing all three sports  N_F +N_(F,V) +N_(F,B) +N_(F,V,B) =65   ...(i)  N_V +N_(F,V) +N_(V,B) +N_(F,V,B) =70   ...(ii)  N_B +N_(F,B) +N_(V,B) +N_(F,V,B) =75   ...(iii)  i+ii+iii:  N_(F,V,B) +2(N_F +N_V +N_B +N_(F,V) +N_(F,B) +N_(V,B) +N_(F,V,B) )−(N_F +N_V +N_B )=210  N_(F,V,B) +2×100−(N_F +N_V +N_B )=210  N_(F,V,B) =10+(N_F +N_V +N_B )  N_(F,V,B) ≥10  i.e. at least 10% children know  playing all three sport games.

Commented by1549442205PVT last updated on 25/Jul/20

Great!Thank you Sir!

Commented byRasheed.Sindhi last updated on 25/Jul/20

Superb! Elegant! MrW Sir!