$$C_1$$ and $$C_2$$ are two hollow concentric cubes enclosing charges $$2Q$$ and $$3Q$$ respectively as shown in figure. The ratio of electric flux passing through $$C_1$$ and $$C_2$$ is

By Gauss law,

$$\Phi=\frac{Q_{enclosed}}{\epsilon_0}$$

For inner cube $$C_1$$, only charge 2Q is enclosed.

$$\Phi_1=\frac{2Q}{\epsilon_0}$$

For outer cube $$C_2$$, both charges 2Q and 3Q are enclosed.

$$\Phi_2=\frac{2Q+3Q}{\epsilon_0}=\frac{5Q}{\epsilon_0}$$

Therefore,

$$\frac{\Phi_1}{\Phi_2}=\frac{2}{5}$$

So ratio is

$$2:5$$

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