Mechanism of a hypothetical reaction
${\mathrm{X}}_2+{\mathrm{Y}}_2\to 2\mathrm{XY}$is given below :

(i) ${\mathrm{X}}_2\to \mathrm{X}+\mathrm{X}$(fast)

(ii)  $\mathrm{X}+{\mathrm{Y}}_2\rightleftharpoons \mathrm{XY}+\mathrm{Y}$ (slow)

(iii) X + Y ➔ XY (fast)

The overall order of the reaction will be

Note : Correct the reactions given in question as 

$$\begin{gathered} {\mathrm{X}}_2\rightleftharpoons \mathrm{X}+\mathrm{X} \left(\mathrm{fast}\right) \\ \mathrm{X}+{\mathrm{Y}}_2⟶\mathrm{XY}+\mathrm{Y} \left(\mathrm{Slow}\right) \\ \text{ Slow step is the rate determining step. } \\ \text{ Rate }=K\left[\mathrm{X}\right]\left[{\mathrm{Y}}_2\right] \left(\mathrm{i}\right) \\ \text{ Equilibrium constant for fast step, }\mathrm{K}=\frac{[\mathrm{X}{]}^2}{\left[{\mathrm{X}}_2\right]} \\ \left[\mathrm{X}\right]=\sqrt{\mathrm{K}\left[{\mathrm{X}}_2\right]} \\ \text{ By substituting }\left[\mathrm{X}\right]\text{ in equation (i), we get } \\ \text{ Rate }=\mathrm{k}\sqrt{\mathrm{K}\left[{\mathrm{X}}_2\right]}\left[{\mathrm{Y}}_2\right]={\mathrm{k}}^{\text{'}}{\left[{\mathrm{X}}_2\right]}^{1/2}\left[{\mathrm{Y}}_2\right] \\ \therefore \text{ Order of reaction }=\frac{1}{2}+1=\frac{3}{2}=1.5 \end{gathered}$$