Two pipes A and B can fill a tank in 48 minutes and 66 minutes, respectively. If both the pipes are opened simultaneously, then after how many minutes should pipe B be closed so that the tank gets filled in 32 minutes?

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Accepted Answer

Step 1: Calculate the rate of filling for each pipe.
- Pipe A fills the tank in 48 minutes, so its rate is 1/48 tank per minute.
- Pipe B fills the tank in 66 minutes, so its rate is 1/66 tank per minute.

Step 2: Let pipe B be open for x minutes and then closed. Pipe A runs for the full 32 minutes.

Step 3: Total work done by both pipes in 32 minutes = 1 tank.

Work done by pipe A in 32 minutes = 32 * (1/48) = 32/48 = 2/3.
Work done by pipe B in x minutes = x * (1/66).

Step 4: Total work = work by A + work by B = 1
=> 2/3 + x/66 = 1

Step 5: Solve for x:
=> x/66 = 1 - 2/3 = 1/3
=> x = 66 * (1/3) = 22 minutes.

Therefore, pipe B should be closed after 22 minutes to fill the tank in 32 minutes.

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