Pipe A can fill a tank in 4 hours, pipe B can fill the same tank in 6 hours and pipe C can fill the same tank in 12 hours. The time taken (in hours) by them to fill half of the same tank if they operate together is:
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Combined rate of the three pipes filling together \(= \dfrac{1}{4} + \dfrac{1}{6} + \dfrac{1}{12}\) tank per hour.
Taking LCM 12: \(\dfrac{3}{12} + \dfrac{2}{12} + \dfrac{1}{12} = \dfrac{6}{12} = \dfrac{1}{2}\) tank per hour.
So together they fill the full tank in \(2\) hours.
Time to fill half the tank \(= \dfrac{1}{2} \times 2 = 1\) hour.
Hence, the three pipes together take 1 hour to fill half of the tank.
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