Question

A pipe can fill a cistern in 12 min and another pipe can fill it in 15 mins. But a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then the third pipe is also opened. Time taken to empty the cistern is:

Answer 1

Let the number of minutes taken to empty the cistern be x min.

According to the question,

x/6−x+5/12−x+5/15=0

x/6−x/12−5/12−x/15−5/15=0

x/6−x/12−x1/5=5/12+5/15

10x−5x−4x/60=25+20/60

x/60=45/60

x=45min