Question

A cistern has a leak which would empty it in 8 hours . A tap is turned on , which admits 6 liters a minutes into the cistern and it is now emptied in 12 hours, How many litres can the cistern hold?

• A. 8000 litres
• B. 8400 litres
• C. 8640 litres
• D. 8650 litres

Answer 1

The correct option is C 8640 litres

Suppose the cistern holds x liters of water.
The tap admits 6 liters of water in 1 minute, i.e., it admits 360 liters of water in 1 hour.
$\therefore$ x liters of water can be filled in $\frac{x}{360}hours$
The leak would empty the tank in 8 hours.
$\therefore$ In one hour, $\frac{1}{8}$ of the tank becomes empty.
If the tap and the leak both are allowed simultaneously, then the tank becomes empty in 12 hours, i.e.,
$\frac{1}{8}-\frac{360}{x}=\frac{1}{12}\Rightarrow \frac{360}{x}=\frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}$
$\Rightarrow x=(360\times 24)liters=8640liters$