Question

Two taps can fill a tank in $30$ minutes and $40$ minutes. Another tap can empty it in $24$ minutes. If the tank is empty and all the three taps are kept open, in how much time the tank will be filled?

Answer 1

Quantity of water filled by the first tap in one minute $=\frac{1}{30}$
Quantity of water filled by the second tap in one minute $=\frac{1}{40}$
Quantity of water emptied by the third tap in one minute $=\frac{1}{24}$
Quantity of water filled in one minute, when all the $3$ taps are opened $=\frac{1}{30}+\frac{1}{40}-\frac{1}{24}$
$=\frac{4+3-5}{120}=\frac{7-5}{120}$
$=\frac{2}{120}=\frac{1}{60}$
Time taken to fill the tank $=\frac{1}{\frac{1}{60}}=60$ minutes
$=1$ hour