The correct option is A X=Na ; Y=Mg
Due to 2p6, noble gas electronic configuration, the second ionisation enthalpy of Na is very high. That's why has large difference between IE1 and IE2 of Mg+ is 2p6,3s1.
After the loss of one electron, Mg2+ will be formed with noble gas electronic configuration. That's why it has less difference between IE1 and IE2.
Thus option (a) is the correct answer.