A tap can fill a cistern in 8 hours and another tap can empty it in 16 hours. If both the taps are opened, then the time taken to fill the tank will be :

Part of   the cistern filled in 1 hour $=\frac{1}{8}$

Part of  the cistern empty in 1 hour $=\frac{1}{16}$

If  both taps are opened simultaneously $\Rightarrow$

$\frac{1}{8}-\frac{1}{16}\Rightarrow \frac{2-1}{16}=\frac{1}{16}hour$

$\therefore$  Cistern can take to fill in 16 hours.