$$\begin{gathered} {\mathrm{Zn}}_{\left(\mathrm{s}\right)}+{\mathrm{Cu}}_{\left(\mathrm{aq}\right)}^{+}\to {\mathrm{Zn}}_{\left(\mathrm{aq}\right)}^{2+}+{\mathrm{Cu}}_{\left(\mathrm{s}\right)};\mathrm{\Delta G}=-\mathrm{XKJ} \\ {\mathrm{Cu}}_{\left(\mathrm{s}\right)}+2{\mathrm{Ag}}_{\left(\mathrm{aq}\right)}^{+}\to 2{\mathrm{Ag}}_{\left(\mathrm{s}\right)}+{\mathrm{Cu}}_{\left(\mathrm{aq}\right)}^{2+};\mathrm{\Delta G}=-\mathrm{YKJ} \\ \text{ then }\left.\mathrm{\Delta G}\text{ for }{\mathrm{Zn}}_{\left(\mathrm{s}\right)}+2{\mathrm{Ag}}_{\left(\mathrm{aq}\right)}^{+}\to 2{\mathrm{Ag}}_{\left(\mathrm{s}\right)}+{\mathrm{Zn}}_{\left(\mathrm{aq}\right)}^{2+}\text{ will be (in }\mathrm{KJ}\right) \end{gathered}$$

$$\begin{gathered} {\mathrm{Zn}}_{\left(\mathrm{s}\right)}+{\mathrm{Cu}}_{\left(\mathrm{aq}\right)}^{+}\to {\mathrm{Zn}}_{\left(\mathrm{aq}\right)}^{2+}+{\mathrm{Cu}}_{(\mathrm{s}{)}^{+}};\mathrm{\Delta G}=-\mathrm{XKJ} \\ {\mathrm{Cu}}_{\left(\mathrm{s}\right)}+2{\mathrm{Ag}}_{\left(\mathrm{aq}\right)}^{+}\to 2{\mathrm{Ag}}_{\left(\mathrm{s}\right)}+{\mathrm{Cu}}_{\left(\mathrm{aq}\right)}^{2+};\mathrm{\Delta G}=-\mathrm{YKJ} \cdots 1 \end{gathered}$$

Now, on subtracting equation 2 from equation 1.

We get, ${\mathrm{Zn}}_{\left(s\right)}+2{\mathrm{Ag}}_{\left(aq\right)}^{+}\to 2{\mathrm{Ag}}_{\left(s\right)}+{\mathrm{Zn}}_{\left(aq\right)}^{2+}$

The Gibbs free energy for this equation is $\mathrm{\Delta G}=-\mathrm{X}-(-\mathrm{Y})=-(\mathrm{X}+\mathrm{Y})$ or $(Y-X)$

Hence, $\mathrm{\Delta G}=-(\mathrm{X}+\mathrm{Y})$

Therefore, option (A) is correct.