Question

Two pipes p and q can fill a tank in 20 hours and 30 hours respectively. both the pipes were opened and just when the tank should have been full, it was noticed that an emptying pipe was also open. the emptying pipe was then closed and it took 6 hours more to fill the tank. in how much time does the emptying pipe empty the tank when it is full?

Answer 1

Acc to the ques, two pipes p and q can fill a tank in 20 hours and 30 hours respectively.

In 1 hr p can fill 1/20 part of the tank.

In 1 hr q can fill 1/30 part of the tank.

So, in 1 hour both the pipes can fill 1/20 + 1/30 part of the tank i.e. 1/12 part.

i.e. Both the pipes can togetherly fill the tank in 12 hours.

Acc to conditioin, In 6 hours both the pipes will fill half of the tank.

Let the pipe r be used for emptying and it takes t hour to empty the tank.

Then, in 1 hour it can empty 1/t part of the tank.

So, half of the tank was filled when three of the pipes were opened and the remaining half by only two pipes.

i.e. 1/12 - 1/t = 1/18

or, 1/t = 1/12 - 1/18

or, 1/t = 1/36

or, t = 36 hours.