Pipes A, B, and C together can fill a tank in 12 hours. Pipes A and B together can fill the same tank in 24 hours. There is another pipe D that can empty this tank in 48 hours. If all the pipes are opened together and after 8 hours pipes A and B are closed then Find the total time taken to fill this tank.

Given:

Pipes A, B, and C together can fill a tank in 12 hours.

Pipes A and B together can fill the same tank in 24 hours.

Pipe D can empty this tank in 48 hours.

Formula Used:

Efficiency = Total work/Total time

Calculation:

Let's assume the capacity of the tank = 48 units (LCM of 12, 24, and 48)

So in 1 hour A, B, and C together can fill = 48/12

⇒ 4 unit 

In 1 hour A, and B together can fill = 48/24

⇒ 2 unit

Then in 1 hour C can fill = 4 - 2

⇒ 2 unit 

Pipe D can empty this tank in 48 hours

So in 1 hour D can empty = 48/48

⇒ 1 unit 

For 8 hours all pipes are opened so they will fill = (4 -1) × 8

⇒ 24 unit

Remaining capacity of tank = 48 - 24

⇒ 24 unit

Now only C and D are open so they will take = 24/(2-1)

⇒ 24 hours 

∴ Total time taken = 8 + 24 = 32 hours