A parallel plate capacitor with air as dielectric is charged to a potential ‘V’ using a battery.  Removing the battery, the charged capacitor is then connected across an identical uncharged parallel plate capacitor filled with wax of dielectric constant ‘k’ . The common potential of both the capacitor is 

Capacitance with air as dielectric $C={\epsilon }_0\frac{A}{d}$
For identical capacitor capacitance with wax as dielectric $C^{\mathrm{\prime }}=\epsilon \frac{A}{d}$
$\therefore C^{\mathrm{\prime }}=KC,\text{ where }K=\frac{\epsilon }{{\epsilon }_o}$
When C and  are conncected in parallel Charge is distributed and the potential Difference is equal for the two capacitors Resultant capacitance $C_R=C+C^{\mathrm{\prime }}$and the total charge Q = CV
Common  potential V=dQ
CR=d CV C+C
$\therefore V=\frac{CV}{C+KC}=\frac{V}{K+1}$