Share

# A Cistern Can Be Filled by a Tap in 4 Hours and Emptied by an Outlet Pipe in 6 Hours. How Long Will It Take to Fill the Cistern If Both the Tap and the Pipe Are Opened Together? - Mathematics

Course
ConceptTime and Work

#### Question

A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 6 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?

#### Solution

$\text{ Time taken by the tap to fill the cistern = 4 hours }$
$\therefore \text{ Tap fills } \frac{1}{4}\text{ th part of the cistern in 1 hour } .$
$\text{ Time taken by the pipe to empty the cistern = 6 hours }$
$\therefore \text{ Pipe empties out } \frac{1}{6}\text{ th part of the cistern in 1 hour } .$
$\text{ Thus, in 1 hour, } \left( \frac{1}{4} - \frac{1}{6} \right)\text { th part of the cistern is filled } .$
$\text{ We have: }$
$\frac{1}{4} - \frac{1}{6} = \frac{6 - 4}{24} = \frac{2}{24} = \frac{1}{12}$
$\text{ Thus, in 1 hour, } \frac{1}{12}\text{ th part of the cistern is filled .}$
$\text{ Hence, the cistern will be filled in 12 hours } .$

Is there an error in this question or solution?

#### APPEARS IN

Solution A Cistern Can Be Filled by a Tap in 4 Hours and Emptied by an Outlet Pipe in 6 Hours. How Long Will It Take to Fill the Cistern If Both the Tap and the Pipe Are Opened Together? Concept: Time and Work.
S