A capacitor has capacitance 5   µ F when its parallel plates are separated by air medium of…

Capacitance of the parallel plate capacitor when air is present $C=\frac{{ϵ}_{0}A}{d}=5 \mathrm{\mu F}$

After insertion of dielectric, the equivalent capacitance of the new capacitor is 

$C_{\mathrm{eq}}=\frac{{ϵ}_0 A}{{\displaystyle \frac{{\displaystyle \frac{d}{2}}}{1.5}}+{\displaystyle \frac{{\displaystyle \frac{d}{2}}}{1}}}$

$=\frac{{\epsilon }_0 A}{\left({\displaystyle \frac{d}{3}}+{\displaystyle \frac{d}{2}}\right)}=\frac{6{\epsilon }_0 A}{5\mathrm{d}}$

$=\frac{6}{5}\times 5 \mathrm{\mu F}=6 \mathrm{\mu F}$.