In a face centerd lattice of X and Y, X atoms are present at the corners while Y atoms are at face centers. Then the formula of the compound is:

$\mathrm{Number} \mathrm{of} \mathrm{X} \mathrm{atoms} \mathrm{occupying} \mathrm{corners} = 8\times \frac{1}{8}=1$

$\mathrm{Number} \mathrm{of} \mathrm{Y} \mathrm{atoms} \mathrm{occupying} \mathrm{face} \mathrm{center}= 6\times \frac{1}{2}= 3$

 $$\begin{gathered} \mathrm{X} :\mathrm{Y} = 1 : 3 \\ \mathrm{So} \mathrm{formula} \mathrm{of} \mathrm{the} \mathrm{compound} \mathrm{is} = {\mathrm{XY}}_3 \end{gathered}$$