# Pipes And Cisterns

Most of the competitive exams are asked related to Pipes and Cisterns and we have a lot of difficulty in solving these questions. In this post we will tell you some important tricks that will help you solve these questions easily. Students practicing Pipes and Cisterns Questions can take help from Formulas for Pipes and Cistern. The higher the work capacity of the Pipes, the faster it can fill or empty. Pipes and Cisterns related questions are asked in almost all types of government job exams. Students can check Pipes and Cisterns Problems with Solutions and its basic concept on this page.

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## Pipes And Cisterns

Pipes And Cisterns Concept

Inlet: A pipe which is used to fill up the tank, cistern or reservoir is known as ‘Inlet’. This type of nature indicates ‘plus’ or ‘positive type’ of work done.

Outlet: A pipe which is used to empty the tank, cistern or reservoir is known as ‘Outlet’. This type of nature indicates ‘minus’ or ‘negative type’ type of work done.

Pipes And Cisterns – Basic Formulas

1. If a pipe can fill a tank in x hours, part filled in 1 hour = 1/x.

2. If a pipe can fill a tank in x hours and another pipe in y hours, part of tank filled in 1 hour when both the pipes are opened simultaneously = (1/x + 1/y) = ( x+y)/xy

∴ Time taken to fill the tank by both the pipes when opened simultaneously = xy/(x+y)

3. If a pipe can empty a tank in “y” hours, then tank emptied in 1 hour = 1/y

4. If a pipe can empty a tank in y hours and another pipe in x hours, part of tank emptied in 1 hour when both the pipes are opened simultaneously = (1/x + 1/y) = (x+y)/xy

∴Time taken to empty the tank by both the pipes when opened simultaneously = xy/(x+y)

5. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, the net part filled in 1 hour = 1/x – 1/y = (y – x)/xy

∴When both the pipes are opened simultaneously, time taken to fill the tank fully = xy/(y – x) hours.

6. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, the net part emptied in 1 hour = 1/y – 1/x = (x – y)/xy

∴ When both the pipes are open simultaneously, time taken to empty the tank fully = xy/(x – y) hours.

Some Pipes and Cisterns Solved Example

Q 1 – Two pipes A and B can fill a tank in 24 hours and 30 hours separately. In the event that both the channel are opened all the while in the void tank, the amount of the truth will surface eventually taken by them to fill it?

1. 12 hrs 10 min
2. 13 hrs 20 min
3. 12 hrs 20 min
4. 11 hrs 20 min

 Explanation:Part filled by A in 1 hour = 1/24, part filled by B in 1 hour = 1/30Part filled by (A+B) in 1 hour = (1/24+ 1/30) = 9/120 = 3/40Time taken by both to fill the tank = 40/3 hrs = 13 hrs 20 min.

Q 2 – A funnel can fill a tank in 15 hours .because of a hole in the bottom; it is filled in 20 hours. On the off chance that the tank is full, what amount of the reality of the situation will become obvious eventually break take to discharge it?

1. 40 hours
2. 50 hours
3. 60 hours
4. 70 hours

 Explanation:Work done by the break in 1 hour = (1/15-1/20) = 1/60Time taken by the break to discharge it = 60 hours

Q 3 – Funnels A and B can fill a tank in 6 hours and 9 hours individually and channel C can purge it in 12 hours. On the off chance that every one of the funnels is opened together in the vacant tank in what amount of the reality of the situation will become obvious eventually be full?

1. 39/7 hrs
2. 36/7 hrs
3. 38/7 hrs
4. 34/7 hrs

 Explanation:Net part filled in 1 hour = (1/6+1/9+1/12) = 7/36Thus, the tank will be full in 36/7 hrs.

Q 4 – Two Pipes A and B can fill a tank in 24 minutes and 32 minutes separately. On the off chance that both the channel opened together, after the amount of time B ought to be shut so that the tank is full in 18 minute?

1. 10 min
2. 8 min
3. 12 min
4. 15 min

 Explanation:Let B be shut after x minutes. At that point, (part filled by (A+B) in x min.)+ {part filled by A in (18-x) min} = 1∴ x (1/24+ 1/32) + (18-X)*1/24 = 1=> 7x/96 + (18-x)/24 =1=> 7x+4(18-x) = 96=> 3x= 24=> x = 8Subsequently, B ought to be shut after 8 min.

Q 5 – Two Pipes A and B can fill a tank in 1 hour and 75 minutes separately. There is likewise an outlet C. On the off chance that all the three funnels are opened together, the tank is full in 50 minutes. What amount of the reality of the situation will become obvious eventually taken by C to purge the full tank?

1. 20 minutes
2. 50 minutes
3. 100 minutes
4. 80 minutes

 Explanation:Work done by C in 1 min. = (1/60 +1/75-1/50) = 3/300 = 1/100Thus, C can discharge the full tank in 100 minutes.

Pipes And Cisterns Short Tricks

1) If two pipes take ‘x’ & ‘y’ hrs respectively to fill the tank and the third pipe takes ‘z’ hrs to empty the tank and all of them are opened together, then

 The net part filled in 1hr = 1 + 1 – 1 x y z

Hence,

 The time taken to fill the tank = 1 (1/x) + (1/y) + (1/z)

2) Consider a pipe fills the tank in ‘x’ hrs. If there is a leakage in the bottom, the tank is filled in ‘y’ hrs.

If the tank is full, the time taken by the leak to empty the tank = 1hrs
 1 – 1 x y

3) Suppose that pipe ‘A’ fills the tank as fast as the other pipe ‘B’. If pipe ‘B’ (slower) & pipe ‘A’ (faster) take ‘x’ min & ‘x/n’ min respectively to fill up an empty tank together, then

 Part of the tank filled in 1 hr = n + 1 x

Pipes And Cisterns Problems With Solutions

Ques1: Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

A) 10 min. 20 sec.

B) 11 min. 45 sec.

C) 12 min. 30 sec.

D) 14 min. 40 sec.

Answer: D) 14 min. 40 sec.

 Explanation:Part filled in 4 minutes =4(1/15+1/20) = 7/15Remaining part =(1-7/15) = 8/15Part filled by B in 1 minute =1/20 : 8/15 :: 1:xx = (8/15*1*20) = 1023min = 10min 40secThe tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

Ques2: A water tank 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) 6 min.to empty

B) 6 min.to fill

C) 9 min.to empty

D) 9 min.to fill

 Explanation:Clearly, pipe B is faster than pipe A and so,the tank will be emptied.part to be emptied = 2/5part emptied by (A+B) in 1 minute=16-110=115115:25::1:x25*15= 6 minsso, the tank will be emptied in 6 min

Ques3: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A) 3 hrs 15 min

B) 3 hrs 45 min

C) 4 hrs 15 min

D) 4 hrs 1

Answer: B) 3 hrs 45 min

 Explanation:Time taken by one tap to fill half of the tank = 3 hrs.Part filled by the four taps in 1 hour =4*1/6 =2/3Remaining part =1-12=1223:12::1:x=> x = 12*1*32=34So, total time taken = 3 hrs. 45 mins.

Ques4: A pump can fill a tank with water in 2 hours. Because of a leak, it took 213 hours to fill the tank. The leak can drain all the water of the tank in:

A) 7 hours

B) 8 hours

C) 12 hours

D) 14 hours

 Explanation:If the total area of pump=1 partThe pumop take 2 hrs to fill 1 partThe pumop take1 hour to fill 1/2 portionDue to lickageThe pumop take 7/3 hrs to fill 1 partThe pumop take1 hour to fill 3/7 portionNow the difference of area = (1/2-3/7)=1/14This 1/14 part of water drains in 1 hourTotal area=1 part of water drains in (1×14/1)hours= 14 hoursSo the leak can drain all the water of the tank in 14 hours.Leak will empty the tank in 14 hrs

Ques5: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in    ?

A) 20 hrs

B) 28 hrs

C) 36 hrs

D) 40 hrs

 Explanation:1/8 – 1/x = 1/10=> x = 40 hrs

Ques6: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

A) 10

B) 12

C) 14

D) 16

 Explanation:Part filled in 2 hours = 2/6=1/3Remaining part =1-13=23(A + B)’s 7 hour’s work = 2/3(A + B)’s 1 hour’s work = 2/21C’s 1 hour’s work = { (A + B + C)’s 1 hour’s work } – { (A + B)’s 1 hour’s work }=1/6-2/21 = 1/14C alone can fill the tank in 14 hours.

Ques7: Three taps A, B and C can fill a tank in 12,15 and 20 hours respectively. If A is open all the time and B, C are open for one hour each alternatively, the tank will be full in:

A) 6 hrs

B) 20/3 hrs

C) 7 hrs

D) 15/2 hrs

 Explanation:A+B’s 1 hour work=112+115=960=320A+C’s 1 hour work=112+120=860=215Part filled in 2 hrs=320+215=1760Part filled in 6 hrs=3*1760=1720Remaining part =1-1720=320Now, it is  the turn of A and B (3/20) part is filled by A and B in 1 hour.Therefore, Total  time taken to fill the tank =(6+1)hrs= 7 hrs

Ques8: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

A) 60 gallons

B) 100 gallons

C) 120 gallons

D) 180 gallons

 Explanation:Work done by the waste pipe in 1 minute =115-120+124=115-11120 = -140 [-ve sign means emptying]Volume of 140 part = 3 gallonsVolume of whole = (3 x 40) gallons = 120 gallons.

Ques9: A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3. The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

A) 50 m^3/min

B) 60 m^3/min

C) 72 m^3/min

D) None of these

 Explanation:Let the filling capacity of the pump be x m3/min.Then, emptying capacity of the pump=(x+10)m3/min.so,2400/x−2400/x+10=8 ⇔x2+10x−3000=0⇒(x−50)+(x+60)=0 ⇔x=50

Ques10: Taps X and Y can fill a tank in 30 and 40 minutes respectively. Tap Z can empty the filled tank in 60 minutes. If all the three taps are kept open for one minute each, how much time will the taps take to fill the tank?

A) 48min

B) 72min

C) 24min

D) None of these

 Explanation:Given taps X and Y can fill the tank in 30 and 40 minutes respectively. Therefore,part filled by tap X in 1 minute = 1/30part filled by tap Y in 1 minute = 1/40Tap Z can empty the tank in 60 minutes. Therefore,part emptied by tap Z in 1 minute = 1/60Net part filled by Pipes X,Y,Z together in 1 minute = [1/30 +1/40 – 1/60] = 5/120 = 1/24i.e., the tank can be filled in 24 minutes.

Ques11: 12 buckets of water fill a tank when the capacity of each tank is 13.5 liters. How many buckets will be needed to fill the same tank,if the capacity of each bucket is 9 liters?

A) 8

B) 15

C) 16

D) 18

 Explanation:Capacity of the tank =(12 x 13.5) liters =162 liters.Capacity of each bucket =9 litersNumber of buckets needed = 162/9 =18.

Ques12: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half ?

A) 31 min

B) 29 min

C) 28 min

D) 30 min

 Explanation:Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24Suppose the tank is filled in x minutes.Then, x/2(1/24 + 1/40) = 1(x/2) * (1/15) = 1 => x = 30 min.

Ques13: One pipe can fill a tank  three times as fast as another pipe. If together the two pipes can fill the tank in 36 min, then the slower alone will be able to fill the tank in:

A) 81 min

B) 108 min

C) 144 min

D) 192 min

 Explanation:Let the slower pipe alone fill the tank in x minutes.Then, faster pipe will fill it in x/3 minutes.=>1/x+3/x=1/36 =>4/x=1/36 =>x=144mins

Ques14: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold ?

A) 360 lit

B) 480 lit

C) 320 lit

D) 420 lit

 Explanation:1/k – 1/20 = -1/24k = 120120 x 4 = 480Therefore, the capacity of the cistern is 480 liters.

Ques15: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 3 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?

A) 8.21 min

B) 8 min

C) 8.57 min

D) 8.49 min

 Explanation:1/10 + 1/15 = 1/6 x 3 = 1/21 – 1/2 = 1/21/10 + 1/15 – 1/x = 1/2x = 8.57 min

Ques16: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes  ?

A) 21 min

B) 24 min

C) 20 min

D) 22 min

 Explanation:Let the pipe B be closed after ‘K’ minutes.30/16 – K/24 = 1 => K/24 = 30/16 – 1 = 14/16=> K = 14/16 x 24 = 21 min.

Ques17: In what time would a cistern be filled by three pipes which diameters are 2 cm, 3 cm and 4 cm running together, when the largest alone can fill it is 58 minutes? The amount of water flowing in each pipe is proportional to the square of its diameter.

A) 26 min

B) 32 min

C) 36 min

D) 42 min

 Explanation:Given that the diameters of the three pipes are 2 cm, 3 cm and 4 cmFrom the given data,Amount of water from three pipes is 4 units, 9 units and 16 units.Let the capacity of cistern be ‘p’ units.∴ p/58 = 16⇒ p = 928 units.In 1 minute, quantity to be filled by 3 pipes = 29 units∴ Total time required = 928/29 = 32 minutes.

Ques18: One fill pipe A is 3 times faster than second fill pipe B and takes 32 minutes less than the fill pipe B. When will the cistern be full if both pipes are opened together?

A) 6 min

B) 8 min

C) 12 min

D) 10 min

 Explanation:Let pipe A takes p min to fillThen,pipe B takes 3p min to fill=> 3p – p = 32=> p = 16 min => 3p = 48 minRequired, both pipes to fill = (48 x 16)/(48 + 16) min = 12 min.

Ques19: Water flows into a tank which is 200 m long and 150 m wide, through a pipe of cross-section (0.3m x 0.2m) at 20 km/h. In what time will the water level be 12m  ?

A) 200 hrs

B) 240 hrs

C) 300 hrs

D) 270 hrs

 Explanation:Volume of water collected in the tank in 1 hour⇒ (0.3 × 0.2 × 20km × 1000mts) = 1200 m cubicIf after t hours, the water is at height of 12m,1200t=200×150×12⇒ t = 300 Hours.

Ques20: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank ?

A) 15 min 20 sec.

B) 16 min 40 sec.

C) 13 min 10 sec.

D) 14 min 40 sec.

Answer: D) 14 min 40 sec.

 Explanation:Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15Remaining part = 1 – 7/15 = 8/15Part filled by B in 1 minute = 1/201/20 : 8/15 :: 1 : kk = (8/15 )x 1 x 20 = 10( 2/3) min = 10 min 40 sec.The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.

Note:

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