If three elements $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are crystallized in cubic solid lattice with $\mathrm{A}$ atoms at corners, $\mathrm{B}$ atoms at cube center and $\mathrm{C}$ atoms at the edges of the cube, which formula of the compound is expected out of the given options?

Atom A is shared by 8 corners. So, 

effective number of atoms of A per unit cell $=8\times \frac{1}{8}=1$

(b) Atom B is present at the cube center. 

So, effective number of atoms of B per unit cell $= 1.$

(c) $\mathrm{C}$ atoms are present at the edges. 1 atom of C is shared by 4 unit cells. So, effective number of atoms 

     of$\mathrm{C}$ per unit cell $=\frac{12}{4}=3.$

Hence, formula of compound $={\mathrm{ABC}}_3$