Answer
$10\ min$
Work Step by Step
Step 1. The taps would fill $1/5$ of the sink per minute.
Step 2. The drain would empty $1/10$ of sink per minute.
Step 3. Together, they would fill $1/5-1/10=1/10$ of the sink per minute.
Step 4. With both working, it will take $\frac{1}{1/10}=10\ min$ to fill the sink.