\(\overline{24X8Y}⋮5\Rightarrow Y=0;5\) but \(\overline{24X8Y}⋮4\Rightarrow Y=0\)

\(\overline{24X80}⋮9\Rightarrow\left(2+4+X+8+0\right)⋮9\Rightarrow\left(14+X\right)⋮9\Rightarrow X=4\)

\(\Rightarrow X+Y=4\)

Hence,the answer is E

24X8Y divisible 5 =. Y = 0 or 5 but 24X8Y divisible => Y = 0

24X80 divisible 9 => (2+4+X+8+0) divisible 9 => (14+X) divisible 9 => X =4

=> The sum  of X and Y is:

   4+0=4