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Pipes A and B can fill an empty cistern in 6 hours and 4 hours respectively, while pipe C can empty the whole cistern in 8 hours. Initially, pipes A and B were simultaneously opened in the cistern. After 2 hours, they were closed and pipe C was opened. After 2 hours, pipe C was also closed. Now, in how much time will the tank be full, if the pipes A and B are simultaneously opened?

Pipes A and B can fill an empty cistern in 6 hours and 4 hours respectively, while pipe C can empty the whole cistern in 8 hours. Initially, pipes A and B were simultaneously opened in the cistern. After 2 hours, they were closed and pipe C was opened. After 2 hours, pipe C was also closed. Now, in how much time will the tank be full, if the pipes A and B are simultaneously opened? Correct Answer 60 min.

Part filled by A in 1 hr. = 1/6

Part filled by B in 1 hr. = 1/4

Part emptied by C in 1 hr. = 1/8

Firstly, pipes A and B are simultaneously opened for 2 hours,

Part filled in 2 hours = 2(1/6 + 1/4) = 2(5/12) = 5/6

Next, pipe C was opened for 2 hours,

Part emptied in 2 hours = 2(1/8) = 1/4

Part of tank that remain filled = 5/6 - 1/4 = 7/12

Now, pipes A and B are opened to fill the tank,

Let they take ‘x’ hrs. to fill the tank,

Part of tank to be filled = 1 - 7/12 = 5/12

⇒ x(1/6 + 1/4) = 5/12

⇒ x(5/12) = 5/12

⇒ x = 1 hr. = 60 min.

∴ The tank will be full in 60 min.

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