Pipes and Cisterns is an important topic for banking exams. Today I am going to share technique to solve questions from this chapter quickly.

### Steps to Solve Pipes and Cistern with Trick:

**Step 1.** Take the LCM of a given Number and that LCM will be the total capacity of cistern or

tank.Place the plus or minus sign for common understanding through picture. plus sign means time taken to fill the cistern and minus sign means to empty the cistern in a particular time.

**Step 2.** Add or Subtract According to a particular question

**Step 3.** The LCM from Step 1. will be the total work . Divide the total capacity of cistern or tank with the outcome of Step 2.

**Important points:**

If pipe can fill the tank in ‘x’ hours then rate of flow is 1/x(1/x portion of tank gets filled in 1 hour)(when we divide the tank into x parts,one part gets filled in a unit of time)

If pipe can empty the tank in ‘y’ hours then emptying rate is 1/y(1/y portion of tank gets emptied in 1 hour)

The rate at which tank is filling =rate of inflow – the rate of outflow.

If a pipe fills the tank at 1/x rate and another pipe empties the tank in 1/y rate then on opening both the pipes :

If (x<y) rate at which tank is is 1/x-1/y

If (x>y) rate at which tank is emptying is 1/y-1/x

## Examples

**#1.**

**Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank ?**

**(M.A.T 2003)**

**Step 1.** Take the LCM of 20 and 30 which is 60. Sixty liter is the total capacity of tank or cistern.

**Step 2.** Divide 60 by (each number) 20 and 30 ,you will get 3 and 2 respectively.

**Step 3.** Now add (3+2) which is 5.

**Step 4.** Now Divide Total capacity of tank or cistern ( 60/5) , you will get Total time taken by them to fill the tank or cistern in a particular time which is in this case is 12 minutes.

**#2. **

**A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously then after how much time will the cistern get filled ?**

**(Hotel management, 1997)**

**Step 1.**Take the LCM of 4 and 9 which is 36. Thirty six liter is the total capacity of tank or cistern.

**Step 2.**Divide 36 by (each number) 4 and 9 ,you will get 9 and 4 respectively.Here plus (+) sign means filling the tank or cistern and minus (-) implies time taken by them to empty the tank.

**Step 3.**Now You see one is filling the tank and other empty it so subtract it with each other.you will get (9-4) 5.

**Step 4.**Now Divide Total capacity of tank or cistern ( 30/5) , you will get Total time taken by them to fill the tank or cistern in a particular time which is in this case is 36/5 minutes.

**#3. **

**Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?**

**(C.B.I, 1997)**

**Step 1.**Take the LCM of 5,10 and 30 which is 30. Thirty liter is the total capacity of tank or cistern.

**Step 2.**Divide 30 by (each number) 5,10 and 30 ,you will get 6,3 and 1 respectively.Here plus (+) sign means filling the tank or cistern and minus (-) implies time taken by them to empty the tank.

**Step 3.**Now you see here each tank is filling the tank in a particular time, so add each value (6+3+1) you will get 10.

**Step 4.**Now Divide Total capacity of tank or cistern ( 30/10) , you will get Total time taken by them to fill the tank or cistern in a particular time which is in this case is 3 hours.

**#4. **

**Pipes A and b can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in ?**

**(Bank P.O. 2002)**