There is a cunducting hollow sphere. We know if we charge it all the charges will stay at the outer surface. But if we drill a hole of radius r(say) then what fraction of the charge will remain inside and outside surface I think it is logical to think that less charge will stay in the inner surface than the outer surface and that more charge will stay inside if the size of hole increases. I attempted to find the solution using Gauss law, by assuming the condition as that of a complete charged sphere with a oppositly charged sphericall circular plane overlayed on it to create hole of charge at that place. But since the electric field won't be uniform, I failed.