Friday, June 22News That Matters

Pipes and Cistern

Important Concepts and Formulas – Pipes and Cistern
Inlet is a pipe connected with a tank or cistern or reservoir. It is used to fill the tank.
Outlet is a pipe connected with a tank or cistern or reservoir. It is used to empty the tank.
If a pipe can fill a tank in  hours,
part of the tank filled in 1 hour If a pipe can empty a tank in  hours,
part of the tank emptied in 1 hour 
If a pipe can fill a tank in x hours and another pipe can fill it in y hours, then both the pipes together can fill the tank in  hours.

Suppose a pipe can fill a tank in  hours and another pipe can empty the full tank in hours. We can examine two cases here.

If <y
net part filled in 1 hour 

If x
net part emptied in 1 hour 

Two pipes A and B can fill a cistern in 75/2 minutes and  minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after
A. 5 min B. 9 min
C. 10 min D. 15 min

Solution 

Pipe A alone can fill the cistern in 75/2 minutes. Since it was open for  minutes, part of the cistern filled by pipe A
4/5

So the remaining 1/5 part is filled by pipe B.

Pipe B can fill the cistern in 45 minutes. So, time required to fill  part
 minutes.

i.e., pipe B is turned off after 9 minutes.

Q. Two pipes P1 and P2 can separately fill a cistern in 20  and 30  minutes respectively and a waste pipe P3 can carry off 22  litres per minute. If all the pipes are opened when the cistern is full, it is emptied in  62 hours. How many litres does the cistern hold?

Q. A tap takes 24  hours extra to fill a tank due to a leakage equivalent to half of its inflow. The inflow can fill in how many hours?

Q. Pipes A and B can fill a cistern in 15 hours together. But if these pipes operate separately A takes 40  hours less than B to fill the tank. In how many hours the pipe A will fill the cistern working alone?

Q. Two pipes can fill a cistern in  15 minutes, 18 minutes respectively. These are opened alternately for 2 min each. In how much time will cistern be filled?

Q. pipe A can fill a tank in 45 minutes and pipe B can empty the tank in 60 minutes. Both pipes are used alternatively for 3 minute. How long will it take to fill the whole tank?

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