A point charge ‘Q’ is placed at a point inside the cone as shown. The flux due to the charge through the curved surface is given as $\frac{2}{3}\frac{\mathrm{Q}}{{\mathrm{\epsilon }}_0}$. the curved surface is given as

${\mathrm{\varphi }}_{\mathrm{base}}+{\mathrm{\varphi }}_{\mathrm{CSA}}=\frac{\mathrm{Q}}{{\mathrm{\epsilon }}_0}$

Now when the second charge is placed the flux because of this from the base is same as ${\mathrm{\varphi }}_{\mathrm{base}}$in the previous case which passes through the curved surface. Hence

${\mathrm{\varphi }}_1+{\mathrm{\varphi }}_2={\mathrm{\varphi }}_{\mathrm{CSA}}+{\mathrm{\varphi }}_{\mathrm{Base}}=\frac{\mathrm{Q}}{{\mathrm{\epsilon }}_0}$