An inlet tap can fill a tank in 20 hours while an outlet tap situated at the bottom of the tank can empty a filled tank in 30 hours. How long will it take to fill an empty tank if the outlet tap is located at one-fourth of the height of the tank from bottom.
Explanation:
Let the work to be done = LCM (20, 30) = 60 units
∴ Efficiency of inlet tap = 60/20 = 3 units/hour Efficiency of outlet tap = 60/30 = -2 units/hour [-ve indicates that the pipe is an outlet pipe]
Since the tap is located at one-fourth of the height from the bottom, it means that till one-fourth of the tank is filled only inlet pipe would be functioning. After that both inlet and outlet pipes would be functioning.
Time to fill one-fourth of the tank = 15/3 = 5 hours [only inlet pipe is functioning]
Time to fill remaining three-fourth of the tank = 45/(3 - 2) = 45 hours [both inlet and outlet pipes are functioning]
∴ Total time taken to fill the tank = 5 + 45 = 50 hours.
Hence, option (b).
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