Question
Pipe A can fill a tank in 50% less time than it takes
pipe B to empty it, while pipe C can fill the same tank in 25% less time than pipe B's emptying duration. If pipe B requires 60 hours to drain the tank completely, how long will it take to fill the tank to 70% of its capacity when pipes A, B, and C operate simultaneously?Solution
Time taken by pipe A alone to fill the empty tank = 60 × 0.50 = 30 hours Time taken by pipe C alone to fill the empty tank = 60 × 0.75 = 45 hours Let the capacity of the tank = 180 litres (LCM of 30, 45 and 60) Quantity of water filled by pipe A alone in one hour = 180/30 = 6 litres Quantity of water filled by pipe C alone in one hour = 180/45 = 4 litres Quantity of water taken out by pipe B alone in one hour = 180/60 = 3 litres So the time taken to fill 70% of the tank = (0.70 × 180)/(6 + 4 – 3) = 18 hours
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