Given that

$$\begin{gathered} {\mathrm{C}}_{\left(\mathrm{s}\right)}+{\mathrm{O}}_{2\left(g\right)}⟶{\mathrm{CO}}_{2\left(g\right)};\Delta {\mathrm{H}}^0=-\mathrm{xKJ} \\ 2{\mathrm{CO}}_{\left(g\right)}+{\mathrm{O}}_{2\left(g\right)}⟶2{\mathrm{CO}}_{2\left(g\right)};\Delta {\mathrm{H}}^0=-\mathrm{yKJ} \end{gathered}$$

The enthalpy of the formation of CO will be

The required equation for the formation of $\mathrm{CO}$ is

 ${\mathrm{C}}_{\left(s\right)}+1/2{\mathrm{O}}_{2\left(g\right)}⟶{\mathrm{CO}}_{\left(g\right)}$

 Upon reversing the equation of the formation of carbon dioxide

 $2{\mathrm{CO}}_{2( \mathrm{g})}⟶2{\mathrm{CO}}_{\left(g\right)}+{\mathrm{O}}_{2\left(g\right)};\Delta {\mathrm{H}}^0=+\mathrm{yKJ}$

 By dividing this equation by 2 , we get

 ${\mathrm{CO}}_{2\left(g\right)}⟶{\mathrm{CO}}_{(g{)}^{+}}1/2{\mathrm{O}}_{2\left(g\right)};\Delta H^0=\frac{y}{2}\mathrm{KJ}$

 Addition of this reaction with the given formation of carbon dioxide reaction, we get

 ${\mathrm{C}}_{\left(s\right)}+1/2{\mathrm{O}}_{2\left(g\right)}⟶{\mathrm{CO}}_{\left(g\right)}=-x+\frac{y}{2}KJ=\frac{y-2x}{2}$

Hence correct option will be (B).