Pipes A and B can empty a full tank in 5 hours and 12 hours respectively and another pipe C can fill the empty tank in 2 hours. If all the three pipes are opened together, then

Given:

Pipe A empties in 5 hours

Pipe B empties in 12 hours

Pipe C fills in 2 hours

Formula Used:

Part emptied/filled in 1 hour = 1 / Total time

Calculation:

Part A empties in 1 hour = 1/5

Part B empties in 1 hour = 1/12

Part C fills in 1 hour = 1/2

Net part filled in 1 hour = (Part C fills) - (Part A empties) - (Part B empties)

⇒ Net part filled in 1 hour = 1/2 - 1/5 - 1/12

⇒ Net part filled in 1 hour = (30 - 12 - 5) / 60

⇒ Net part filled in 1 hour = 13 / 60

Time taken to fill the tank = 1 / (Net part filled in 1 hour)

⇒ Time taken = 60 / 13 hours

∴ The tank will be filled in  60 / 13 hours.