Initial total charge of the system is: Qi=Q1+Q2=CV+2CV=3CV
When dielectric is inserted in C so the capacitance becomes KC
Final charge, Qf=Q′1+Q′2=KCV′+2CV′=(K+2)CV′ where V′= common potential after disconnected the battery.
As battery is disconnected so total charge will remain unchanged.
Thus, Qi=Qf⇒3CV=(K+2)CV′
∴V′=3VK+2