Question
Pipe ‘X’ can fill a cistern in 15 hours while pipe
‘Y’ can drain the cistern in 25 hours. Both pipes are opened at the same time, but pipe ‘Y’ is shut off after 5 hours. How long will pipe ‘X’ take to fill the rest of the cistern?Solution
ATQ,
Let the total capacity of the cistern be 75 litres {LCM (15 and 25)}
Efficiency of pipe ‘X’ = (75 / 15) = 5 litres/hour
Efficiency of pipe ‘Y’ = (75 / 25) = 3 litres/hour
Water filled in 5 hours by both pipes = 5 × (5 – 3) = 10 litres
Time taken by pipe ‘X’ to fill remaining cistern = (75 – 10) / 5 = 13 hours
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