A crystalline solid is made of X, Y and Z. Atoms of X are present...

Number of X-atoms in unit cell = 4
Number of Y-atoms = 4
Number of Z atoms = 8
If atoms along one body diagonal are removed then 2 from corners X, 1 from body center Y and 2 neat two corners Z atoms will be absent.
Effective number of atoms may be calculated as
$X = 4 - 2 \times \dfrac{1}{8} = \dfrac{15}{4}$
$Y = 4 - 1 = 3$
$Z = 8 - 2 = 6$
Simplex ratio $= X: Y: Z$
$= \dfrac{15}{4}: 3: 6$
$= 5: 4: 8$
Simplest formula $= {X}_{5}{Y}_{4}{Z}_{8}$.