Pipes A and B can fill a tank in 6 hours and 8 hours respectively and pipe C can empty the full tank in 12 hours. All three pipes are opened together, but pipe A is closed after 3 hours. In how many hours will the remaining part of the tank be filled?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 9.
Pipe A's 1-hour work = 1/6
Pipe B's 1-hour work = 1/8
Pipe C's 1-hour work = -(1/12)
(A + B + C)'s 3-hour work = 3 (1/6 + 1/8 - 1/12) = 3 (6/24) = 3/4
remaining part = 1 - 3/4 = 1/4
Let in x hours 1/4 part of the tank will be filled by B and C.
⇒ x(1/8 - 1/12) = 1/4
⇒ x(1/24) = 1/4
⇒ x = 6
total time = 3 + 6 = 9 hours