Pipe ‘A’ and pipe ‘B’ can fill a cistern in 15 minutes and 36 minutes respectively. Pipe ‘C’ alone can empty the cistern in 12 minutes. If all three pipes are opened together then what is the time taken to fill 50% of the cistern?
Let the capacity of the cistern = 180 units Then, efficiency of pipe ‘A’ = 180/15 = 12 units/minute Efficiency of pipe ‘B’ = 180/36 = 5 units/minute Efficiency of pipe ‘C’ = 180/12 = 15 units/minute So, combined efficiency of pipes ‘A’, ‘B’ and ‘C’ = 12 + 5 – 15 = 2 units/minute 50% of the cistern’s capacity = 90 units Therefore, time taken by all 3 pipes together to fill 50% of the cistern = 90/2 = 45 minutes
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