A cistern has two supply pipes A,B and a waste pipe C. Through A and B, the cistern can be filled in 15 minutes and 18 minutes respectively. Through C the full cistern can be emptied in 20 minutes. At first the pipes A and C are opened for 5 minutes. Then the pipe A is closed and the pipe B is opened. How much time is needed to fill the cistern?????
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Answers
Answer:
A cistern has two supply pipes A,B and a waste pipe C. Through A and B, the cistern can be filled in 15 minutes and 18 minutes respectively. Through C the full cistern can be emptied in 20 minutes. At first the pipes A and C are opened for 5 minutes. Then the pipe A is closed and the pipe B is opened. How much time is needed to fill the cistern?????
Explanation:
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Answer:
2¾ hours
Explanation:
Time taken by Pipe A to fill = 15 mins
Time taken by Pipe B to fill = 18 mins
Time taken by Pipe C to empty = 20 mins
Work done by Pipe A in a minute = 1/15
Work done by Pipe B in a minute = 1/18
Work done by Pipe C in a minute = -(1/20)
Work done by Pipe A and Pipe C together in a minute = 12/180 - 9/180 = 3/180
Work done by Pipe B and Pipe C together in a minute = 10/180 - 9/180 = 1/180
So , work done by Pipe A and Pipe C together for 5 minutes = 5 × 3/180 = 15/180
So , time taken = 180/180 - 15/180 = 165 minutes