# Pipe & Cistern Tricks & Tips

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Problems containing pipes and cisterns fall broadly into one of two categories. The first category being one wherein questions are concerned with the time required to fill up a tank, with a combination of one or more pipes and cisterns. The second category, concerns itself with leakages and holes, requiring you to calculate the effective rate of the tank being filled or emptied.

**Type 1: Pipes and Cistern (Tank)**

**Type 1: Pipes and Cistern (Tank)**

In order to solve questions falling into the first category, imagine each of the pipes as a human doing some work. (Again, we are using a Work and Time reference here). The time taken by a single pipe to fill up the tank by itself, is the time taken by that human to do the entire work. Find out each pipe’s (or human’s) rate of doing work, with respect to each other. For instance, if Pipe A can fill the tank in 8 hours, and Pipe B can fill it in 4 hours, you know that the rate of B is twice that of A.

Once, you have the rates of doing work, all you have to do is add them up to find out the overall rate of filling the tank by all the pipes together. Remember, rate is always inversely proportional to the time taken, so the rates you add up should be reciprocals of the time taken by each pipe.

An easy tip that helps, is to assign any one pipe’s rate as ‘x’, and calculate the others’ rate in terms of ‘x’.

** E.g. 1.** Pipe A fills a tank in 3½ hours whereas Pipe B fills the same tank in 10½ hours.

__Solution__*:*

__Solution__*:*

Since Pipe B takes more time, let us take ‘x’ as the rate at which B fills the tank.

Since time taken by B is 3 times the time taken by A, the rate of A will be 3 times faster than the rate of B. So the rate of A is ‘3x’.

REMEMBER: RATE, NOT TIME!! |

Another advantage of using the rates, is that **rates** can be added up, not **time**. Which means that if two pipes take 4 and 8 hours respectively to fill up a tank, you can add the reciprocals of 4 and 8 to get the net rate. What you **cannot** do, is add 4 and 8 up, directly. That would result in a wrong answer.

The logic is simple. If you add 4 and 8 up, to find the time taken by both together to fill up the tank, you will get 12. But think, if one pipe takes 4 hours and the other takes 8 hours to fill up the tank, they couldn’t possibly take 12 hours together! When in doubt, use this trick!

So let us use the rates in the following example:

** E.g. 2.** Pipes P, Q, R and S can fill a certain tank in 3, 5, 6 and 10 hours, respectively. How much time will it take for the tank to be filled if all pipes are opened together?

__Solution__*:*

__Solution__*:*

Let ‘x’ be the rate of Pipe S, which is the slowest. So the rates of all the pipes are as follows. Make sure to make as few calculations as possible – this is the trick to cracking your exam! Try the following method:

Pipe |
Time Taken (in hours) |
Efficiency (Inverse of time) |

S | 10 | x (where x=1/10) |

Q | 5 (1/2 of 10) |
2x |

P | 3 (1/3.33 of 10) |
3.33 x |

R | 6 (2 times 3) |
1.66x (1/2 of 3.33x) |

So the total efficiency of the four pipes is: x + 2x + 3.33x + 1.66x ≈ 8x = 8 × (1/10)

Thus the total time taken for the four pipes working together to fill the tank would be:

**10/8 hours = 1.25 hours = 1 hour 15 mins.**

** **

__Shorten Your Calculations__

__Shorten Your Calculations__

By choosing the pipe taking the maximum time first and basing your calculations on that, you effectively bring down the number of reciprocal calculations you make. Of course, you need to pick and choose which pipe’s efficiency to calculate next. Like in the example, after S, we chose Q because its time taken was a direct multiple of the time taken by S. This lets us calculate its reciprocal easily. Next, we were left with Pipes P and R, both of whose times are not multiples of the time taken by S. However, we all know that 10 is 3.33 times 3. So we use this to first find the efficiency of P. Next we know that 6 is two times 3. So clearly the efficiency of R is half of P.

**In Pipe And Cistern Type-1, I am going to discuss some important Pipe And Cistern Problem Shortcut Tricks .**

(Q1)Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively.If both pipes are opened together, the time taken to fill the tank is.

**Solution: Fig.**

**Rate of Filling the tank by A and B in 1 minute=3+2=5 unit**

**So, total time taken by Pipe (A+B)=60/5**

** =12 minutes Ans.**

**[Concept:** **First step-L.C.M=20,30=60 i.e total unit. now 60/20=3 unit per minutes tank filling by pipe A and 60/30=2 unit per minutes tank filling by pipe B.]**

(Q2) A tap can empty a tank in 30 minutes. A second tap can empty it in 45 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?

**Solution: Fig.**

**Rate of emptying the tank by 1st and 2nd tap in 1 minute=(3+2)**

** =5 unit**

**So, total time taken by (1st+2nd)tap=90/5**

** =18 minutes Ans.**

**[Concept:** **First step-L.C.M=30,45=90 i.e total unit. now 90/30=3 unit per minutes tank emptying by 1st tap and 90/45=2 unit per minutes tank emptying by 2nd tap.]**

(Q3)Three tapes A, B, C can fill an overhead tank in 4, 6 and 12 hours respectively. How long would the three taps take to fill the tank if all of them are opened together?

**Solution: Fig.**

**Rate of Filling the tank by A, B and C in 1 hour=(3+2+1)**

** =6 unit**

**So, total time taken by (A+B+C)=12/6**

** =2 hours Ans.**

**Common Type Of Pipe And Cistern Problem Shortcut Tricks That Are Frequently Asked In Various Competitive Exam like SSC CGL, SSC CHSL, FCI etc. Type-1.1 **

(Q1)A water tank can filled by a tap in 30 minutes and another tap can fill it in 60 minutes. If both the taps are kept open for 5 minutes and then the first tap is closed, how much time 2nd tap will take to fill the remaining tank.

**Solution: Fig.**

**Rate of Filling the tank by 1st tap and 2nd tap in 1 minute=(2+1)**

** =3 unit**

**[Concept: From fig.**

**According to question 1st tap and second tap को 5 minutes तक एक साथ खुला रखा गया है तो दोनों 5 minutes में कितना water fill करेगा वो निकाल लेंगे| 5 minutes के बाद तो 1st tap बंद कर दिया जा रहा है तो सिर्फ अब tank के remaining unit को fill करने के लिए 2nd tap ही बचा है तो वो कितना time लेगा वो निकाल लेंगे. ]**

**Rate of Filling the tank by 1st tap and 2nd tap in 5 minute=5×3=15 unit**

**Remaining=60-15=45 unit that is filled by 2nd tap**

**So, total time taken by 2nd tap=45/1**

** =45 minutes Ans.**

(Q2)Three pipes A, B and C can fill a tank in 6 hours, 9 hours and 12 hours respectively. B and C are opened for half an hour, then A is also opened. The time taken by the three pipes together to fill the remaining part of the tank is.

**Solution: Fig.**

**Rate of Filling the tank by A+B+C in 1 hour=(6+4+3)unit**

** =13 unit**

**[ Concept: From fig.**

**half an hour तक B and C tank fill करेगा |half an hour के बाद A को open किया जाता है तो अब A, B and C मिलकर करेगा| ]**

**Rate of Filling the tank by B+C in 1 hour=(4+3)unit**

** =7 unit**

**Rate of Filling the tank by B+C in half an hour=7/2 unit**

**Remaining unit=36-(7/2)=65/2 unit**

**So, total time taken by (A+B+C)=(65/2)/13**

**=2 ½ hours Ans.**

(Q3)Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the tank in 8 hours. The time(in hours) in which the tank can be filled by pipe C alone is.

**Solution:**

**Let tank fill by A+B+C in 1 hour= 1 unit**

**Tank fill by A+B+C in 6 hour= 6 unit**

**After working together for 2 hours then**

**Tank fill by A+B+C in 2 hour= 2 unit**

**Remaining = 6 – 2=4 unit that is filled by A and B because C is closed**

**Rate of filling of A+B in 1 hour=4/8=0.5 unit**

**Rate of filling of C in 1 hour=1-0.5=0.5 unit**

**Time taken by C = 6/0.5= 12 hours Ans.**

**Common Type Of Pipe And Cistern Problem Shortcut Tricks That Are Frequently Asked In Various Competitive Exam like SSC CGL, SSC CHSL, FCI etc. Type-1.2 **

(Q1)A tank has two pipes. The first pipe can fill it in 4 hours and the second can empty it in 16 hours. If two pipes are opened together at a time, then the tank will be filled in.

**Solution: Fig.**

**Rate of filling the tank by 1st pipe= 4 unit per hour**

**Rate of emptying the tank by 2nd pipe= 1 unit per hour**

**Net rate of filling the tank=4-1=3unit**

**so required time=16/3=5 ¹/3 hours Ans.**

**[concept:****जब एक pipe tank को fill(भर)कर रहा हो or दूसरा empty(खाली) कर रहा हो तो जो pipe tank को fill कर रहा होगा, तो उसका Rate of filling the tank (+ve) में लेना है or जो pipe tank को empty कर रहा होगा तो उसका Rate of emptying the tank ( -ve) में लेना है| इसलिए figure में +ve or -ve लिया गया है.]**

(Q2)Two pipes A and B can fill a cistern in 3 hours and 5 hours respectively. Pipe C can empty in 2 hours. If all the three pipes are open, in how many hours the cistern will be full?

**Solution: Fig.**

**Rate of filling a cistern by A= 10 unit per hour**

**Rate of filling a cistern by B= 6 unit per hour**

**Rate of emptying a cistern by C= -15 unit per hour**

**Net rate of filling the tank by (A+B-C)=10+6-15**

** =1 unit per hour**

**so total time taken by (A+B-C)=30/1**

** =30 hours Ans.**

**Common Type Of Pipe And Cistern Problem Shortcut Tricks That Are Frequently Asked In Various Competitive Exam like SSC CGL, SSC CHSL, FCI etc. Type-1.3**

(Q1)Two pipes A and B can fill a tank with water in 30 minutes and 45 minutes respectively. Another pipe C can empty the tank in 36 minutes. First A and B are opened. After 12 minutes, C is also opened. The tank is filled up in.

**Solution: Fig.**

**[ Concept: From fig.**

** ]**

**Rate of filling the tank by (A+B) in 1 minute=(6+4)=10 unit**

**Rate of filling the tank by (A+B) in 12 minute=12×10=120 unit**

**Remaining=180-120=60 unit that is filled by A, B and C**

**Rate of emptying the tank by C = -5 unit per minute**

**Net rate of filling the tank by (A+B-C)=(6+4-5)**

** =5unit per minute**

**so required time taken by (A+B-C)=60/5**

** =12 minutes**

**Total time=12+12=24 minutes Ans.**

**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.

## 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)**

## Practice Questions

### Ques 1.

Two pipes P and Q can fell a cistern in 24 min. and 36 min. respectively . Third pipe R can empty it in 36 min. If all the three pipes are opened , find the taken to fill the cistern.

(a) 1 hour

(b) 24 mins

(c) 36 mins

(d) 30 mins

### Ques 2.

A tank has a leak which would empty it in 8 hours. A tap is turned on which admit 6 liters a minute into the tank and it now emptied in 12 hours . How many literes does the tank holds?

(b) 8640 ltr

(c) 8560 ltr

(d) 8800 ltr

### Ques 3.

(a) 8 min. 34 sec.

(b) 7 min.10 sec.

(c) 12 min.

(d) 10 min

### Ques 4.

Two pipes can fill a tank in 10 minutes and 30 minutes respectively and a third pipe can empty the full tank in 20 minutes . If all the three pipes are opened simultaneously, the tank will be filled in:

(a) 12 minutes

(b) 10 minutes

(c) 8 minutes

(d) 6 minutes

### Ques 5.

Two pipes can fill a cistern in 14 hours and 16 hours respectively . The pipes are opened simultaneously and it is found that due to leakage in the bottom , 32 minutes extra are taken for the cistern to be filled up. When the cistern is full , in what time will the leak empty it ?

(a) 108 hours

(b) 112 hours

(c) 116 hours

(d) 120 hours

### Ques 6.

(a) 17 min

(b) 171/7 min.

(c) 17 2/7 min.

(d) 18 min.

### Ques 7.

If two pipes function simultaneously , the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir?

(a) 20 hours

(b) 25 hours

(c) 30 hours

(d) 40 hours

### Ques 8.

A tank is filled in hours by three pipes A, B and C . The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

(a) 40 hours.

(b) 35 hours

(c) 30 hours

(d) 25 hours

### Ques 9.

(a) 16 hours

(b) 14 hours

(c) 12 hours

(d) 10 hours

### Ques 10.

Three taps P, Q and R can fill a tank in 12, 15 and 20 hours respectively . If P is opened all the time and Q and R are opened for one hour each alternately , the tank will be full in

(a) 5 hours

(b) 6 hours

(c) 6 2/3 hours

(d) 7 hours

### solutions:

**Ans 1.**Since time taken to fill the cistern by Q = time taken to empty the cistern by R so

**Ans 2**. In I hour the part filled by the tap = 1/8 -1/12 = 1/24

Hence , the tap can fill the tank in 24 hours.

Therefore, capacity of the tank = 24 x 60 x 6 = 8640 litres.

**Ans 3**. The waste pipe can empty in 1 min .= 1/10 + 1/12 – 1/15 = 11/60 – 1/15 = 7/60

of the cistern.

Hence, the waste pipe can empty the cistern in 60/7 minutes , i.e., 8 minutes 34 sec.

**
Ans 4**. 1n I minute the part filled by all the three pipes = 1/10 + 1/30 – 1/20 = 1/12

Hence , all the three pipes will fill the bank in 12 minutes.

**Ans 5.** In I hour the part filled by both the pipes = 1/14 + 1/16 = 15/112

Hence, both the pipes will fill the cistern in 112/15 min.

but due to leakage , the tank will be filled in 112/15 + 32/60 = 120/15 = 8 hours.

Since, in 1 hr. the part emptied by the leakage = 15/112 – 1/8 = 1/112

Therefore , leakage will empty the tank in 112 hours.

**
Ans 6**. In 1 minute the part filled by the three pipes = 1/12 + 1/10 -1/8 = 7/120

Hence, all the three pipes will fill the cistern in 120/7 = 17 1/7 minutes.

**Ans 7**.Let ( x- 10) and x hrs be the time taken by two pipes to fill the reservoir , then,

Hence , second pipe will fill the reservoir in 30 hours.

**
Ans 8.**Let x,x/2 and x/4 hours be the time taken by pipes A, B and C respectively to

Hence , time taken by A is 35 hours to fill the tank.

**Ans 9.**In 2 hour the part filled by all the three pipes = 2 X 1/6 = 1/3

Remaining part = 1 – 1/3 = 2/3, which is filled by ( P + Q ) in 7 hours.

Hence , in 1 hour the part filled by ( P + Q ) = 2/ 3 x 7 = 2/21

Since , in 1 hour the part filled by R alone = 1/6 – 2/21= 1/14

Therefore, R alone will fill the bank in 14 hours.

**Ans 10**.In 1 hour the part filled by (P + Q ) = 1/12 + 1/15 = 3/20

In 1 hour the part filled by (P + R ) = 1/12 + 1/20 = 2/15

Hence, in 2 hours the part filled by ( P+ Q +R ) = 3/20 + 2/15 = 17/60

Then , in 6 hours the part filled by ( P + Q + R ) = 3 x 17/60 = 17/20

Remaining part = 1 – 17/20 = 3/20 , which is filled by ( P + Q ) in 1 hour.

Hence, total time taken = 6 + 1 = 7 hours.

**CISTERN:**

Cistern is referred to a tank/Reservoir which has some specific capacity to hold liquid.

**PIPES:**

There are two types of Pipes,They are

1)Inlet Pipe

2)Outlet Pipe

**Inlet Pipe:**

Inlet Pipe is used to fill the tank.

**Outlet Pipe:**

Outlet Pipe is used to empty the tank.

There may be any number of Inlet Pipes and Outlet Pipes that are connected to a cistern.

Total Capacity=LCM(Given Numbers)(unit-Litres)

Time=Total Capacity/Efficiency(unit-hr,sec,min,day)

Efficiency=Total Capacity/Time(unit Litre/hour)

## #.1.TYPE 1:

### PROBLEMS BASED ON INDIVIDUAL CAPACITY:

There are 3 sub type in this type,they are

1)When both the pipes are Inlet Pipes

2)When both the pipes are Outlet Pipes

3)One Pipe is Inlet Pipe and Outlet Pipe

**1)When both the pipes are Inlet Pipes:**

**1)Pipe A can fill the tank in 10 hrs and Pipe B can fill the tank in 40 hrs.How long will it take to fill the tank if both the pipes are opened?**

Given that,

Pipe A can fill the tank in 10 hrs and Pipe B can fill the tank in 40 hrs

Total Capacity=LCM(10,40)=40Litres

A’s Efficiency=40/10=4 litre/hour

B’s Efficiency=40/40=1 litre/hour

So,

When both are opened,their total capacity=4+1=5 Litre/hour

**Time=40/5=8 hours**

So,When Pipe A and B are opened together,they can fill the tank in 8 hours

**2)When both the pipes are Outlet Pipes:**

**1)Pipe A can empty the tank in 3 hours where as Pipe B can empty the tank in 6 hours.When they opened together how,long will it take to empty the tank?**

**Given that,**

Pipe A can empty the tank in 3 hours where as Pipe B can empty the tank in 6 hours.

Total Capacity of the tank=LCM(3,6)=6 Litres

A’s Efficiency=6/3=2litres/hour

B’s Efficiency=6/6=1 litre/hour

Total Efficiency of (A+B)=(2+1=3litres/hour)

Time=6/3=2hours

**Therefore,When A & B are opened together,they can empty the tank in 2 hours**

**3)One Pipe is Inlet Pipe and Outlet Pipe:**

**1)A can fill the tank in 12 hours,B can empty the tank in 15 hours.When both the pipes are opened find how long will it take to empty/fill the tank ?**

Given that,

A can fill the tank in 12 hours,B can empty the tank in 15 hours

Total Capacity=LCM(12,15)=**60 Litres**

A’s(Inlet Pipe) Efficiency=60/12=5litre/hour

B’s(Outlet Pipe)Efficiency=60/15=4litre/hour

Note:

**If the Efficiency of Inlet Pipe is greater then the Outlet Pipe the tank will be filled,**

**If the Efficiency of Outlet Pipe is greater then the Inlet Pipe then the tank will be Emptied**

Inlet Pipe fill 5 litre in 1 hour at the same time Outlet Pipe empty 4 Litre in 1 hour so,in 1 hour only 1 litre is filled in the tank.

**Time taken to fill the tank=60/1=60hours**

## #.2.TYPE 2:

### BASED ON PARTIAL WORK:

**1)Pipe A can fill the tank in 15 minutes and Pipe B can fill the tank in 20 Minutes.They opened together for 4 Minutes and after that B was turned off.How long will A take to fill the Remaining tank capacity?**

Given that,

Pipe A=15 minutes(fill)

Pipe B=20 minutes(fill)

Total Capacity=LCM(15,20)=60litres

Efficiency of A=60/15=4litre/min

Efficiency of B=60/20=3litre/min

They were Opened for 4 Minutes,

4+3=7litre/min

7*4=28 Litre.

Remaining 60-28=32 litre

After that B was turned off,then 32 litre is filled by Pipe A

=32/4=**8 min**

## #.3. TYPE 3:

### BASED ON EFFICIENCY:

1)A is thrice as efficient as B,If both the pipes are opened together the tank is filled in 2 days,then how long will it take to fill the tank only if Pipe B is Opened?

Let us Assume the capacity of Pipe B=10litre/day

Therefore,Capacity of Pipe A=3(B)

=3(10)=30litre/day

So When they are opened together,they can fill 40 litres/day

In 2 days,they can fill 80litres

If **Pipe B is Opened then it will take-80/10=8 days**

## #.4. TYPE 4

### BASED ON TIME:

1)There are 4 inlet Pipes namely A,B,C,D and their individual capacity to fill the tank is 20 hours,30 hours,40 hours and 50 hours respectively.A opens at 6.00 A.M.,B opens at 8.00 A.M.,C opens at 9 A.M. and D opens at 10 A.M.Find at what time the tank will be filled?

Total Capacity=LCM(20,30,40,50)=600 Litres

A’s Efficiency=600/20=30litres/hour

B’s Efficiency=600/30=20litres/hour

C’s Efficiency=600/40=15 litres/hour

D’s Efficiency =600/50=12 litres/hour

Given that,

A is opened at 6.00 A.M. till 10.00 A.M,it is opened for 4 hours

=30*4=120 litres/hour

B is opened at 8.00 A.M. till 10 A.M.,it is opened for 2 hours

=20*2=40 litres/hour

C is opened at 9.00 A.M. till 10 A.M., it is opened for 1 hour

=15*1=15 litres/hour

At 10.00 A.M

Three Pipes (A,B & C fill 175 litres)

Remaining Capacity in the tank=600-175=425 litres

This 475 litres is filled by all the 4 Inlet Pipes

Time=475/(30+20+15+12)

=475/77

=5 hours 30 Minutes

So from 10 A.M. it would take 5 hours 30 Minutes

**The tank will be filled at 3.30 P.M**

## #.5 TYPE 5:

### BASED ON PARTIAL TIME:

1)Two Pipes A & B fill the tank in 60 Minutes and 40 Minutes respectivley.How many minutes will it take to fill the tank from empty state if B is used for half the time & A and B used to fill Other half?

Let the Total Capacity=LCM(60,40)=120 Litres

Efficiency of A=120/60=2 litre/minute

Efficiency of B=120/40=3 litre/minute

Let the time taken by the pipes to fill the tank be X

Half the time=X/2 is used to fill the tank by B & Another half the time is used to fill the tank by A+B

=X/2(Filled by Pipe B)+X/2(Filled by Pipe A+B)

=(X/2)* (3) + (X/2)* (5)

=3(X/2) + 5(X /2)

=8(X/2)

We know that

Total Capacity=Time * Efficiency

120 = (X/2) * 8

240=X*8

30=X

**Therefore, the tank is filled in 30 Minutes**

**What a typical question looks like?**

In such questions, basically a tank has to be filled by two (or more) pipes and we are given:

**1)** Time taken by each pipe to fill the tank.

**2)** Total time taken to fill the tank

We’re, usually, given either of the aforementioned information & we’ve to find out the other.

The problem with maximum difficulty asked for Pipes & Cistern can be described in the image below:

Here, we’ve a ‘**Tank’** around which the whole question revolves. Basically, we’ve to find out in how long the ** whole tank could be filled or emptied**. Then there are

**Inlet Pipes (A and B),**there can any number of Inlet pipes.

**Inlet pipes are responsible for filling the tank**. They, basically, ** bring the water in**.

*The work*

*done by them is positive*.

Then we an **Outlet pipe**, there can be any number of outlet pipes too. Outlet pipes are responsible for emptying the tank. They, basically, __put the water out.__ *The work done by them is negative.*

**Rules for solving such questions:**

**1.** If a pipe can fill the tank in ‘x ’ hours then, the part filled in 1 hour = 1/x

**2. **If a pipe can empty the tank in ‘ y’ hours then, the part emptied in 1 hour = 1/y

**3.** If a pipe can fill the tank in ‘x ’ hours and another can empty it in ‘*y*’ hours then, the **net part filled in 1 hour = 1/x – 1/y ; Total time taken to fill such tank = xy/y-x**

**4. **If three such pipes are there where ‘x’, ‘y’ are inlet and ‘z’ is outlet, Total Time =

**5**. A pipe can fill the tank in ‘x’ hrs. Due to leak it is filled in ‘y’ hrs, time taken by leak to empty the tank** =xy/y – x hrs**

**6.** If leak time > Inlet pipe then tank will be filled; If leak time < Inlet pipe then tank will be emptied.

**Sample Questions:**

**Qs. 1 – **Pipe A can fill the tank in 20 hours while Pipe B alone can fill it in 30 hours and Pipe C can empty the tank in 40 hours. If all the pipes are opened together, in how long will the tank be full?

**Solutions – **Net part filled in 1 hour = 1/20 + 1/30 – 1/40 (as work done by C is negative)

= 7/120

⇒ Full tank will be full in ** 120/7 = 17 1/7 hours.**

**Q2.** There’s a leak in the bottom of tank. When the tank is thoroughly repaired, it would be filled in 3.5 hours. It now takes half an hour longer. If tank is full, how long would it take to leak the tank?

**Sol.** Here, clearly the ‘**leak’** is working like an **Outlet pipe**.

**Done using rule 5)**

We need to find the time taken to empty tank by leak (or outlet pipe) if tank is full

Repaired tank is filled in 3.5 hours ⇒ Inlet pipe takes 3.5 hours

Un-repaired tank takes 3.5+0.5 = 4 hrs ⇒ time taken 4 hours to fill tank.

Total time taken to empty such tank **= xy/y-x = 3.5 x 4 / 4 – 3.5 = 28 hrs. **

Leak would empty the cistern in 28 hours.

**Q3.**Two pipes P and Q would fill tank in 24 hours and 32 hrs respectively. If both pipes are opened together, find when the first pipe must be turned off so that the tank may be just filled in 16 hrs?

**Sol.** Suppose the pipe P is closed after ‘x’ hours.

Then, P pipe would fill in 1 hr = 1/24 and in x hrs = x / 24

Pipe Q would fill in 1 hour = 1 / 32 and in 16 hrs (as tank is full in 16 hrs) = 16 /32 = 1/2

Pipe P work in ‘x’ hr + Pipe Q work in 16 hrs = 1 (as they complete the 1 unit of work) = x/24 + 16/32 = 1

⇒ x = 12 hours.

__Short method:__

The first pipe should work for =

**Q4.** Three pipes A, B and C can fill cistern in 6 hrs. After working together for 2 hrs, C is closed and A & B fill it in 8 hrs. Then find the time in which cistern can be filled by pipe C.

**Sol:** A + B + C work in 1 hr = 1/6 of cistern

A+B+C work in 2 hr = 1/6

A+B+C work in 2 hr = 1/6 × 2 = 1/3 of cistern

Unfilled part after 2 hrs = 1 – 1/3 = 2/3 of Cistern

This 2/3 of cistern is filled by A & B in 8 hrs.

⇒ A & B can fill the full cistern in = 8×3/2 = 12 hrs

We know that A+B+C = 6 hrs

C = (A+B+C) – (A+B) = (1/6) – (1/12) = 1/12

**⇒ C alone would fill it in 12 hrs.**

**Q5.** A tank has a leak which would empty it in 8 hrs. A tap is turned on which admits 6 liters a minute into tank, and it’s now emptied in 12 hrs. How many liters does the tank hold?

**Sol.** Time by Outlet Pipe = 8 hrs

Tank emptied in = 12 hrs

**Done using rule 5)**

Time by Inlet pipe = (12×8)/(12 – 8) = 24 hrs.

Also given: Inlet pipe takes 6 liters in a minute ⇒ In 1 hr, intake = 6×60 = 360L

⇒ Intake in 24 hrs =** 360×24 = 8640 liters**

Hence, the total capacity of tank is **8,640 L.**

**Note:** If it’s given that tank takes 8 hrs to get full but with leak it takes 2 hrs more, then 8 hrs is the time taken by Inlet pipe and 10 hrs is total time to fill with leak.

**Qs. 6***. *A can fill tank in 12 minutes, B in 15 minutes and C empties it in 6 minutes. A and B are opened for 5 minutes then C is also opened. In what time is the tank empty?

**Sol.** A + B in 5 minutes = [1/12 + 1/15]×5 = ¾

⇒ 3/4^{th} part of tank is filled in 5 minutes.

When C is also opened, work done by all pipes in 1 minute = **1/12 + 1/15 – 1/6 = 1/60 **

When all three are opened, the tank is emptied in 60 minutes.

So, 3/4 part will be emptied in **= 60 x 3/4 = 45 minutes**

**Q7.** Two pipes can separately fill a tank in 20 hrs and 30 hrs respectively. Both the pipes are opened to fill the tank but when tank is 1/3 full a leak is developed in the tank through which 1/3 of water supplied by both the tank leak out. What is total time taken to fill the tank?

**Sol**. Time taken by two pipes to fill the tank = (20×30)/(20+30) = 12 hrs.

1/3^{rd} tank is filled in = 12×1/3 = 4 hrs; Left time = 12 – 4 = 8 hrs.

Now, leakage develops which empties 1/3^{rd} of water supplied (by both pipes)

⇒ Now, efficiency of Inlet pipes = 1 – 1/3 = 2/3^{rd} .

Earlier, at 1 efficiency they were taking 8 hrs

now at 2/3^{rd} efficiency they will take 8 ÷ 2/3 = 12 hrs

⇒ Total time taken to fill the tank= 4 + 12 = 16 hrs

# Practice Problems on **Pipes and Cistern**

**Pipes and Cistern**

**A Special pump can be used for filling as well as for emptying a Cistern. The capacity of the Cistern is 2400m³. The emptying capacity of the Cistern is 10m³ per minute higher than its filling capacity and the pump needs 8 minutes lesser to Cistern the tank than it needs to fill it. What is the filling capacity of the pump?**

A. 40m³/min

B. 50m³/min

C. 60m³/min

D. 30m³/min

E. None of the Above**Three pipes P, Q and R can fill a Cistern in 6 hours. After working at it together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the Cistern is**

A. 14 hours

B. 12 hours

C. 15 hours

D. 18 hours

E. None of the Above**A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?**

A. 5 minutes

B. 4 minutes

C. 6 minutes

D. 8 minutes

E. None of the Above**If a pipe A can fill a tank 3 times faster than pipe B. If both the pipes can fill the tank in 32 minutes, then the slower pipe alone will be able to fill the tank in?**

A. 128 minutes

B. 124 minutes

C. 154 minutes

D. 168 minutes

E. None of the Above**A large cistern can be filled by two pipes P and Q in 15 minutes and 20 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?**

A. 12 minutes

B. 17 minutes

C. 18 minutes

D. 19 minutes

E. None of the Above**A pipe can fill a cistern in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the cistern completely?**

A. 3 hours

B. 2 hours

C. 9 hours

D. 4 hours

E. None of the Above**Two pipes P and Q are opened together to fill a tank. Both the pipes fill the tank in time “x” If Q separately took 25 minutes more time than “x” to fill the tank and Q took 49 minutes more time than “x” to fill the tank, then find out the value of x?**

A. 48 minutes

B. 35 minutes

C. 54 minutes

D. 68 minutes

E. None of the Above**Three taps P, Q and R can fill a tank in 12, 15 and 20 hours respectively. If P is open all the time and Q, R are open for one hour each alternatively, the tank will be full in**

A. 3 hours

B. 2 hours

C. 7 hours

D. 4 hours

E. None of the Above**Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. If both the pipes were kept open when the tank is empty, how much time will it take for the tank to overflow?**

A. 3 minutes

B. 2 minutes

C. 5 minutes

D. 4 minutes

E. None of the Above**Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 5 hours to fill up the whole tank. After how many hours Q was closed?**

A. 14 hours

B. 15 hours

C. 10 hours

D. 16 hours

E. None of the Above

**If a pipe A can fill a tank 3 times faster than pipe B and takes 32 minutes less than pipe B to fill the tank. If both the pipes are opened simultaneously, then find the time taken to fill the tank?**

A. 14 minutes

B. 12 minutes

C. 15 minutes

D. 16 minutes

E. None of the Above**Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 8 minutes?**

A. 14 minutes

B. 12 minutes

C. 15 minutes

D. 18 minutes

E. None of the Above**A full tank gets emptied in 8 minutes due to the presence of a leak in it. On opening a tap which can fill the tank at the rate of 9 L/min, the tank get emptied in 12 min. Find the capacity of a tank?**

A. 120 L

B. 240 L

C. 216 L

D. 224 L

E. None of the Above**If a pipe A can fill a tank 3 times faster than pipe B. If both the pipes can fill the tank in 42 minutes, then the slower pipe alone will be able to fill the tank in?**

A. 148 minutes

B. 124 minutes

C. 154 minutes

D. 168 minutes

E. None of the Above**A large cistern can be filled by two pipes P and Q in 15 minutes and 10 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?**

A. 6.5 minutes

B. 7.5 minutes

C. 8.5 minutes

D. 9.5 minutes

E. None of the Above**A pipe can fill a cistern in 8 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the cistern completely?**

A. 3 hours

B. 2 hours

C. 5 hours

D. 4 hours

E. None of the Above**Two pipes P and Q are opened together to fill a tank. Both the pipes fill the tank in time “x” If Q separately took 16 minutes more time than “x” to fill the tank and Q took 36 minutes more time than “x” to fill the tank, then find out the value of x?**

A. 48 minutes

B. 24 minutes

C. 54 minutes

D. 68 minutes

E. None of the Above**A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the cistern completely in 1 hour 20 minutes when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is plugged. If there is a leakage also which is capable of draining out the water from the tank at half of the rate of the outlet pipe, then what is the time taken to fill the empty tank when both the pipes are opened?**

A. 3 hours

B. 2 hours

C. 5 hours

D. 4 hours

E. None of the Above**A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the cistern completely in 1 hour 20 minutes when the outlet pipe is plugged. The outlet pipe empties the tank completely in 4 hours when the inlet pipe is plugged. If both pipes are opened simultaneously at a time when the tank was one-third filled, when will the tank fill thereafter?**

A. 3 hours

B. 2 hours

C. 5 hours

D. 4 hours

E. None of the Above**Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 8 hours to fill up the whole tank. After how many hours Q was closed?**

A. 4 hours

B. 5 hours

C. 2 hours

D. 6 hours

E. None of the Above

**Three pipes A, B, and C can fill the tank in 10 hours, 20 hours and 40 hours respectively. In the beginning all of them are opened simultaneously. After 2 hours, tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by tap A alone. What is the percentage of the work done by tap A alone?**

A. 30 %

B. 35 %

C. 45 %

D. 50 %

E. None of the Above**A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?**

A. 30 mins

B. 25 mins

C. 45 mins

D. 50 mins

E. None of the Above**Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?**

A. 72 hours

B. 62 hours

C. 64 hours

D. 84 hours

E. None of the Above**A tank is normally filled in 6 hours but takes two hours longer to fill because of a leak in the bottom of the tank. If the tank is full the leak will empty it in how many hours?**

A. 16 hours

B. 18 hours

C. 17 hours

D. 24 hours

E. None of the Above**Twelve pipes are connected to a Cistern. Some of them are inlet pipes and the others are outlet pipes. Each of the inlet pipes can fill the tank in 8 hours and each of the outlet pipes can empty the cistern completely in 6 hours. If all the pipes are kept open, the empty tank gets filled in 24 hours. How many inlet pipes are there?**

A. 6

B. 8

C. 7

D. 4

E. None of the Above**A dam has four inlets – A, B, C and D. The dam can be filled in 12 minutes through the first three inlets and it can be filled in 15 minutes through the second, the third and fourth inlet also it can be filled through the first and the fourth inlet in 20 minutes. How much time required to fill up the dam by all the four inlets?**

A. 10 mins

B. 15 mins

C. 20 mins

D. 25 mins

E. None of the Above**Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?**

A. 2 hours

B. 3 hours

C. 4 hours

D. 5 hours

E. None of the Above**A Cistern can be filled by an inlet pipe at the rate of 4 litres per minute. A leak in the bottom of a cistern can empty the full tank in 8 hours. When the cistern is full, the inlet is opened and due to the leak, the cistern is empty in 40 hours. How many litres does the cistern hold?**

A. 4000 litre

B. 2400 litre

C. 1920 litre

D. 2020 litre

E. None of the Above**In a tank there is a pipe which can be used for filling the tank as well as for emptying it. The capacity of the tank is 1200 m³. The emptying of the tank is 10 m³ per minute higher than its filling capacity and the pump needs 6 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pipe?**

A. 20 m³ / min.

B. 40 m³ / min.

C. 50 m³ / min.

D. 60 m³ / min.

E. None of the Above**Two pipes P and Q can fill a cistern in 12 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours will the tank be full?**

A. 4 hours

B. 5 hours

C. 2 hours

D. 6 hours

E. None of the Above

**Two pipes A and B can fill a tank in 10 hours and 15 hours respectively while a third pipe C can empty the full tank in 20 hours. All the pipes are opened for 5 hours and then C is closed. Find the time in which the tank is full?**

a) 5.5 hrs

b) 6.5 hrs

c) 7.5 hrs

d) 8.5 hrs

e) None of these**Three pipe P, Q and R can fill a tank in 12 minutes, 18 minutes and 24 minutes respectively. The pipe R is closed 12 minutes before the tank is filled. In what time the tank is full?**

a) 8.(5/13) hrs

b) 8.(4/13) hrs

c) 7.(4/13) hrs

d) 8.(6/13) hrs

e) None of these**On pipe P is 4 times faster than pipe Q and takes 45 minutes less than pipe Q. In what time the cistern is full if both the pipes are opened together?**

a) 8 minutes

b) 10 minutes

c) 12 minutes

d) 14 minutes

e) None of these**Two pipes can fill a tank in 15 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to the leakage in the bottom, 17/7 hours extra are taken extra to fill the tank. If the tank is full, in what approximate time would the leak empty it?**

a) 27 hrs

b) 32 hrs

c) 36 hrs

d) 39 hrs

e) None of these**Two pipes A and B can fill a tank in 8 minutes and 12 minutes respectively. If both the pipes are openedsimultaneously, after what time should B be closed so that the tank is full in 6 minutes?**

a) 1 min

b) 2 min

c) 3 min

d) 4 min

e) None of these**In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.**

a)10.5 minutes

b) 11.5 minutes

c) 12.5 minutes

d) 13.5 minutes

e) None of these**Two pipes P and Q can fill a tank in 10 min and 12 min respectively and a waste pipe can carry off 12 litres of water per minute. If all the pipes are opened when the tank is full and it takes one hour to empty the tank. Find the capacity of the tank.**

a) 30

b) 45

c) 60

d) 75

e) None of these**One pipe fill 1/4 of the tank in 4 minutes and another pipe fills 1/5 of the tank in 4 minutes. Find the time taken by both pipe together to fill half the tank?**

a) 40/9 minutes

b) 50/9 minutes

c) 44/9 minutes

d) 53/9 minutes

e) None of these**Two pipes can separately fill the tank in 15hrs and 30hrs respectively. Both the pipe are opened and when the tank is 1/3 full a leak is developed due to****which 1/3 water supplied by the pipe leaks out. What is the total time to fill the tank?**

a) 20/3 hr

b) 35/3 hr

c) 40/3 hr

d) 50/3 hr

e) None of these**Three pipes A, B and C is attached to a cistern. A can fill it in 20 minutes and B can fill it in 30 minutes. C is a waste pipe. After opening both the pipes A and B, Riya leaves the cistern to fill and returns when the cistern is supposed to be filled. But she found that waste pipe C had been left open, she closes it and now the cistern takes 5 minutes more to fill. In how much time the pipe C can empty the full cistern?**

a) 26.8 minutes

b) 25.8 minutes

c) 27.8 minutes

d) 28.8 minutes

e) None of these