Pipe A can fill a cistern in 4 hours and Pipe B can fill the same cistern in 5 hours. Pipe C can empty a full cistern in 3 hours. If all three pipes are opened together, then the time (in minutes) taken to fill the tank is: (round to the nearest minute)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 514.
Pipe A and Pipe B can fill the cistern in 4 hours and 5 hours. Pipe C can empty the full cistern in 3 hours.
So, Pipe A fills 1/4 of the cistern in 1 hour and Pipe B fills 1/5 of the cistern in 1 hour.
Also, Pipe C empties 1/3 of the cistern in 1 hour.
Net work per hour = (Work done by A + Work done by B) - Work done by C
= (1/4 + 1/5) - 1/3
= 7/60
Time required to fill the cistern = 1/(7/60) = 60/7 hours
= (60/7) × 60 minutes
= 514.29... minutes
= 514 minutes (approx)
Therefore, three pipes will take 514 minutes to fill the cistern.