​ A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps ​

Question

A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already \(\frac{1}{2}\) full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled completely or emptied completely, as the case may be?

Answer 1

In one minute, \(\frac{1}{16}\) - \(\frac{1}{8}\) = - \(\frac{1}{16}\) of the tank can be filled, i.e.,\(\frac{1}{16}\) of the whole tank can be emptied.

\(\therefore\) The whole tank can be emptied in 16 minutes.

Since the tank is half full, therefore it will be emptied in 8 minutes.