Question
An inlet pipe can fill a tank in 18 minutes, while an
outlet pipe can empty it in 27 minutes. Sujata starts the inlet pipe at 6 a.m., but the outlet pipe is accidentally opened at the same time. She notices the mistake at 6:15 a.m. and closes the outlet pipe. At what time will the tank be completely filled?Solution
Let the volume of the tank (LCM 0f 18 and 27) = 54 units So, the inlet pipe fills in 1 minutes = 54/18 = 3 units And the 0utlet pipe empties in 1 minutes = 54/27 = 2 units For the first 15 minutes both the inlet and outlet pipe are working. Hence, it will fill in starting 15 minutes = 15× (3-2) = 15 unit Remaining volume of the tank = 54-15 = 39 units Now this 39 units is to be filled by inlet pipe Time taken to fill the remaining part of tank = 39/3 = 13 minutes time to fill the tank completely filled = 6:15 + 13 minutes = 6:28 a.m.
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