Question
Two pipes X and Z can fill a tank in 36 hours and 48 hours
respectively, while pipe Y can drain the tank in 72 hours. If pipes X and Z are opened together for 10 hours and then Z is closed and Y is opened, how long will it take to completely fill the tank?Solution
ATQ,
Let capacity of the tank = 288 litres (LCM of 36, 48, and 72)
Water filled by pipe X in 1 hour = 288 / 36 = 8 litres
Water filled by pipe Z in 1 hour = 288 / 48 = 6 litres
Water drained by pipe Y in 1 hour = 288 / 72 = 4 litres
In first 10 hours, X and Z together fill:
= 10 × (8 + 6) = 10 × 14 = 140 litres
Remaining volume to be filled = 288 – 140 = 148 litres
Now only pipes X and Y are open, so effective rate = 8 – 4 = 4 litres/hour
Time to fill remaining tank = 148 / 4 = 37 hours
Total time taken = 10 + 37 = 47 hours
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