Let $\phi _A$, $\phi _B$ and $\phi _C$ are the electric flux linked with A, B and C.

According to Gauss theorem,

$\phi _A + \phi _B + \phi _C$ = ${q \over {{\varepsilon _0}}}$

Since $\phi _A$ = $\phi _C$

$\Rightarrow 2{\phi _A} = {q \over {{\varepsilon _0}}} - {\phi _B}$

$\Rightarrow 2{\phi _A} = {q \over {{\varepsilon _0}}} - \phi$   $\left( {Given\,{\phi _B} = \phi } \right)$

$\therefore$ ${\phi _A} = {1 \over 2}\left( {{q \over {{\varepsilon _0}}} - \phi } \right)$