A tap can fill a tank in 20 min. another can empty it in 16 min. If the tank is already half full and both are opened together. How long it will take to empty the tank?

Time taken to fill the tank $=\frac{1}{20}\min$

Time taken to empty the tank $=\frac{1}{16}\min$

Work done by both in 1 min $=\frac{1}{20}-\frac{1}{16}$

$=\frac{4-5}{80}=\frac{-1}{80}$ [$-Ve$means empty]

$\therefore$ Full tank emptied in 80 min

$\therefore$ Half tank in 40 min.