A compound is formed by two elements A and B. The element B forms cubic close packed structure and atoms of A occupy $\frac{1}{3}$ of tetrahedral voids. If the formula of the compound is ${\mathrm{A}}_{\mathrm{x}}{\mathrm{B}}_{\mathrm{y}}$, then the value of $\mathrm{x}+\mathrm{y}$ is in option

The number of effective atoms per unit cell in the cubic close packed arrangement is 4. Hence, there are four atoms of $\mathrm{B}$ per unit cell. In cubic close packed arrangement, there are two tetrahedral voids per atom. So, eight tetrahedral voids are possible. Given that $1/3$ of tetrahedral voids are occupied. Hence, the possible formula is 

${\mathrm{A}}_{\frac{8}{3}}{\mathrm{B}}_4$ and the simplest formula is ${\mathrm{A}}_8{\mathrm{B}}_{12}\equiv {\mathrm{A}}_2{\mathrm{B}}_3$.

So, $\mathrm{x}=2 \& \mathrm{y}=3$

$\Rightarrow \mathrm{x}+\mathrm{y}=5$