Question

Two taps can fill a tank in $20$ minutes and $30$ minutes respectively. There is an outlet tap at exactly half lever of that rectangular tank which can pump out $100$ litres of water per minutes if the outlet tap is open, then it takes $24$ minutes to fill an empty tank, What is the volume of the tank ?

• A. $1800$ litres
• B. $1500$ litres
• C. $1200$ liters
• D. $2400$ litres

Answer 1

The correct option is A $1800$ litres

Part of the tank that can be filled by the two filler taps $=$ $(\frac{1}{30}+\frac{1}{20})=\frac{2+3}{60}=\frac{5}{60}=\frac{1}{12}$
$\therefore$ The two taps can fill the tank in $12$ minutes.
$\Rightarrow$ half of the tank will be filled in $6$ minutes.
$\Rightarrow$ The time taken by the remaining half of the tank to be filled when the outlet pipe is open $=(24-6)$ min $=18$ min.
$\Rightarrow$ Part of that half of the tank that can be emptied in $1$ hour $=$ $\frac{1}{6}-\frac{1}{18}=\frac{1}{9}$
$\therefore$ Time taken to empty half of the cistern $=9$ minutes
$\therefore$ Capacity of the tank $=100\times 9\times 2=1800$ liters.