Two elements A and B combine to form a compound in which ‘a’ gram of A combines with $\text{'}{b}_1\text{'}$and $\text{'}{b}_2\text{'}$gm of B. According to law of multiple proportion, 

Mass of element A is fixed i.e., a gram.

Masses of element B are $b_1$and $b_2$

According to law of multiple proportions, masses of element that combine with fixed mass of another element must bear a simple whole number ratio. 

Therefore, $b_1 and b_2$bear a simple whole number ratio.