For the process

$$\begin{gathered} {\mathrm{X}}_{\left(\mathrm{g}\right)}+{\mathrm{e}}^{-}\to {\mathrm{X}}^{-}\left(\mathrm{g}\right),\mathrm{\Delta H}=\mathrm{x}\text{ and } \\ {\mathrm{X}}_{\left(\mathrm{g}\right)}^{-}\to {\mathrm{X}}_{\left(\mathrm{g}\right)}+{\mathrm{e}}^{-},\mathrm{\Delta H}=\mathrm{y} \\ \mathrm{Select} \mathrm{correct} \mathrm{alternate} : \end{gathered}$$

We know that ionization potential is the minimum energy required to remove most loosely held the outermost shell in the ground state from an isolated gaseous atom and,

Electron affinity is the amount of energy released when an electron is added to the outermost shell of one mole of an isolated gaseous atom in its lower energy state.

So,

$\mathrm{X}\left(\mathrm{g}\right)+{\mathrm{e}}^{-}\to {\mathrm{X}}^{-}\left(\mathrm{g}\right);\Delta \mathrm{H}=\mathrm{x}=\mathrm{EA}$ of $\mathrm{X}\left(\mathrm{g}\right)$

${\mathrm{X}}^{-}\left(\mathrm{g}\right)\to \left(\mathrm{X}\right)\mathrm{g}+{\mathrm{e}}^{-};\Delta =\mathrm{y}=\left(\mathrm{IE}\right)$ of ${\mathrm{X}}^{-}\left(\mathrm{g}\right)$

=-(E A) of X(g)

Hence, option(d) is the answer.