Question

A cistern can be filled by pipes A and B in 4 hours and 6 hours respectively. When full, the cistern can be emptied by a pipe C in 8 hours. If all the pipes be turned on at the same time, the cistern will be full in what time ?​

Answer 1

Net filling in 1 hour = (1/4 + 1/6 - 1/8) = 7/24

∴ Time taken to fill the cistern = (24/7) hrs. = 3 hrs. 26 min.

Answer 2

Step-by-step explanation:

water filled in one hour by tap A = 1/4th

water filled in one hour by tap B = 1/6th

therefore in one hour if both taps A and B are opened

simultaneously, then in one hour both taps can fill

1/4 + 1/6 = (3 + 2)/12 => 5/12th of the tank

now tap C takes 8 hours to empty the tank, therefore

tap C in one hour can empty 1/8th of the tank

when all three taps are opened at the same time, then

in one hour level of water in the tank in one hour is,

5/12 - 1/8 => (10 - 3)/24 => 7/24th of tank

therefore the time taken for the tank to be full is

reciprocal of 7/24 => 24/7 hours

=> 3 hours 26 minutes