A quarter of the balls are red and therefore there are 360 x (1 / 4) = <<360*(1/4)=90>>90 red balls.
When you remove the red balls from the ball pit there are 360 - 90 = <<360-90=270>>270 remaining balls
A fifth of the remaining balls are blue, and therefore there are 270 x (1 / 5) = <<270*(1/5)=54>>54 blue balls.
The total of red and blue balls equals 90 + 54 = <<90+54=144>>144 balls
When you remove the red and blue balls from the total there are 360 - 144 = <<360-144=216>>216 balls that are neither red nor blue.
#### 216