'a' and 'b'

For both $\frac{a}{b}$ and $\frac{b}{a}$ to be integers, a must be equal to b. Because if a is not equal to b then: If $a>b$ then $\frac{a}{b}>1$ and $\frac{b}{a}<1$ . So they cant both be integers. If $a<b$ by the same logic they cant both be integers. So $a=b$ with $a>20$ and $b<100$ . So, b can take values from 21 to 99. Hence, we have 79 different values of b.