Nicole ate 2/5 of the total number of cookies, which is 2/5*600= <<2/5*600=240>>240
The total number of cookies that remained in the box after Nicole ate 240 is 600-240 = <<600-240=360>>360
Eduardo then ate 3/5 of the remaining cookies, a total of 3/5*360 = <<3/5*360=216>>216 cookies
The total number of cookies that remained after Eduardo ate 216 is 360 - 216 = <<360-216=144>>144
The percentage of the cookies that remained out of the original amount is 144/600*100% = 24%
#### 24