Question

There are two taps to fill a tank and a third to empty it. When the third tap is closed, they can fill the tank in $10$ minutes and $12$ minutes respectively. If all the three taps are opened, the tank is filled in $15$ minutes. If the first two taps are closed, in what time can the third tap empty the tank when it is full ?

• A. $8\frac{4}{7}$ min
• B. $7\frac{4}{7}$ min
• C. $9\frac{4}{7}$ min
• D. $4\frac{4}{7}$ min

Answer 1

The correct option is A $8\frac{4}{7}$ min

Let the third tap take $x$ minutes to empty the tank. Then,
$\frac{1}{10}+\frac{1}{12}-\frac{1}{x}=\frac{1}{15}\Rightarrow \frac{1}{x}=\frac{1}{10}+\frac{1}{12}-\frac{1}{15}=\frac{6+5-4}{60}=\frac{7}{60}$
$\therefore$ The third tap takes $\frac{60}{7}$ min $=8\frac{4}{7}$ min to empty the tank.