A compound formed by elements A and B crystallizes in a cubic structure where A atoms are at the corners of a cube and B atoms are at the face centers of the cube. The formula of the compound is

A cube has atoms at its four corners.
So, the amount of A atoms in each cell.$=8\times \frac{1}{8}=1$

The centres of the faces of a cube also contain B atoms.
So,the quantity of B atoms per unit cell

$=6\times \frac{1}{2}=3$

Hence option B is correct