Answer     7

Rewrite the given expression as $$\frac{n}{30-n}=\frac{30 - (30-n)}{30-n}=\frac{30}{30-n} - 1$$

Then, in order for it to be a positive integer, $\frac{30}{30-n}$ must be an integer greater than $1$. We know $30$ has $8$ positive factors. Therefore the denominator $30-n$ has $8$ choices to make $\frac{30}{30-n}$ a positive integer, $7$ of which will make the result greater than $1$. Hence, the answer is $7$.