Question
Pipe A alone and pipe C alone can fill the empty tank in
50% less time and 25% less time respectively than the time taken by pipe B to empty the full tank. If the time taken by pipe B alone to empty the full tank is 72 hours, then in how many hours would the tank be 84 litres filled if the pipes A, B and C are opened together?Solution
Time taken by pipe A alone to fill the empty tank = 72 × 0.50 = 36 hours
Time taken by pipe C alone to fill the empty tank = 72 × 0.75 = 54 hours
Let the capacity of the tank = 216 litres (LCM of 36, 54 and 72)
Quantity of water filled by pipe A alone in one hour = 216 / 36 = 6 litres
Quantity of water filled by pipe C alone in one hour = 216 / 54 = 4 litres
Quantity of water taken out by pipe B alone in one hour = 216 / 72 = 3 litres
So the time taken to fill 84 litres of the tank = 84 / (6 + 4 – 3) = 84 / 7 = 12 hours
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