In fig , 1,2 have capacitance C .when a dielectric k is intro in one of them what is total charge flowing through the battery

Before adding the dielectric, net capacitance of the circuit=.
Hence total charge on the capacitors=

After adding dielectric, the capacitance of one of the capacitor becomes.
Hence effective capacitance of the circuit becomes

Hence total charge on the capacitors increases to
Hence amount of charge flown out of the battery=
Hence answer is option D.