A compound is formed by two elements A and B. The element B forms...

The number of effective atoms per unit cell in the cubic close packed arrangement is 4. Hence, there are four atoms of $B$ 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

$A\dfrac{8}{3}{B}_{4}$ and the simplest formula is ${A}_{8}{B}_{12} ≡ {A}_{2}{B}_{3}$.

So, $x = 2 \text{ and } y = 3$

$⇒ x + y = 5$