A crystal is made up of particles $X,Y,$ and $Z$. $X$ forms fcc packing. Y occupies all octahedral voids of X and Z occupies all tetrahedral voids of X. If all the particles along one body diagonal are removed, then the formula of the crystal would be 

For fcc, number of X atoms = 4/unit cell 
Number of TVs = 8Z
Number of OVs = 4Y
Number of atoms removed along one body diagonal $=2X$ (corner) and 2Z(TVs) and IY (OV at body centre)

$\therefore$ Number of X atoms left $=4-(2\times \frac{1}{8})=\frac{15}{4}$

Number of Y atoms left  $=4-(1\times 1)=3$
Number of Z atoms left  $=8-(2\times 1)=6$
The simplest formula  $=X_{\frac{15}{4}}{Y}_3{Z}_6\Rightarrow X_{15}{Y}_{12}{Z}_{24}$
$\Rightarrow X_5{Y}_4{Z}_8$