Question

A pipe can fill a cistern in 12 minutes and another pipe can fill it in 15 minutes but a third pipe can empty it in 6 minutes. the first two pipes are kept open for 5 minuted in the brginning and then the third pipe is also openef. time taken to empty the cistern is

Answer 1

LCM(12,15,6) = 60

Assume the cistern contain 60 litre of water. Then,

Amount of water filled by the first pipe in 1 min = 6012=56012=5 litre
Amount of water filled by the second pipe in 1 min = 6015=46015=4 litre
Amount of water emptied by the third pipe in 1 min = 606=10606=10 litre

First two pipes were open for 5 min. Due to this,
amount of water filled = 5(5 + 4) = 45 litre.

Now all pipes are open. Therefore, amount of water emptied in 1 min
= 10 - (5 + 4) = 1 litre

So, 45 minutes are required to empty 45 litre.