A ring of charge with uniform charge density is completely enclosed in a hollow donut shape. An exact copy of the ring is completely enclosed in a hollow sphere.
A) What is the ratio of the flux out of the donut shape to that out of the sphere?

Explanation:

According to Gauss's theorem , total flux coming out of a closed surface area is equal to 1/ε₀ times charge enclosed

This flux coming out of enclosed charge does not depend upon the shape of enclosing surface area . It only depends upon the charge enclosed .

It the present context , in both the case ie in case of donut or sphere , since amount of charge enclosed  is same , flux coming out too will be same in both the case

Hence the required ratio = 1 : 1