In the circuit shown, charge on the $5 mu mathrm{F}$ capacitor is :

Let $q_{1}$ and $q_{2}$ be the charge on the capacitors of $2 \mu \mathrm{F}$ and $4 \mu \mathrm{F}$. Then charge on capacitor of $5 \mu \mathrm{F}$

$Q=q_{1}+q_{2}$

$\Rightarrow 5 V_{0}=2\left(6-V_{0}\right)+4\left(6-V_{0}\right)$

$\Rightarrow 5 V_{0}=12-2 V_{0}+24-4 V_{0}$

$\Rightarrow 11 V_{0}=36 \Rightarrow V_{0}=\frac{36}{11} V$

$\Rightarrow Q=5 V_{0}=\frac{180}{11} \mu C$