Question
There are 3 inlet and (z-1) outlet pipes attached to a
tank. Each inlet pipe takes 40 hours to fill the tank, and each outlet pipe empties the fully filled tank in 16 hours. If all the pipes are opened together, the tank gets filled in 20 hours. Find the value of 'z'.Solution
ATQ, Total work = 80 units (LCM of 40 and 16) Inlet efficiency = 2 units Outlet efficiency = -5 units Total efficiency of inlet = 3 × 2 = 6 units Total efficiency of outlet = -5 (z – 1) = (-5z + 5) units ATQ: => (6 - 5z + 5) × 20 = 80 => (11 - 5z) = 80/20 => 11 - 5z = 4 => -5z = 4 - 11 => -5z = -7 => z = 7/5
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