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- 1. SREENIVASA INSTITUTE OF TECHNOLOGY AND MANAGEMENT STUDIES Murukambattu Post, Chittoor – 517 127 (A.P)AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY – ANANTAPUR, Course material For Reasoning and Quantitative Aptitude Module Name: PIPES AND CISTERNS Page 1
- 2. PREREQUISITES:1. Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet. Outlet: A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.2. If a pipe can fill a tank in x hours, then: 1 part filled in 1 hour = . x3. If a pipe can empty a tank in y hours, then: 1 part emptied in 1 hour = . y4. 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, then 11 the net part filled in 1 hour = - . xy5. 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, then the net part emptied in 1 hour = 1-1 . 6.Time for filling , (Filling pipe is bigger in size.) F = (e * f)/(e - f) Page 2
- 3. 7.Time for emptying , (emptying pipe is bigger in size.) E = (f * e)/(f - e)8.Pipes A & B can fill a tank in f1hrs & f2hrs respectively.Another pipe C can empty thefull tank in ehrs.If the three pipes are opened simultaneously then the tank is filled in F = L/[(L/f1) + (L/f2) - (L/e)]9.Two taps A & B can fill a tank in t1 & t2 hrs respectively.Another pipe C can empty thefull tank in ehrs.If the tank is full & all the three pipes are opened simultaneously . Then thetank will be emptied in, E = L/[(L/e) - (L/f1) - (L/f2)]10.A filling tap can fill a tank in fhrs.But it takes ehrs longer due to a leak at the bottom.Theleak will empty the full tank in , E = [t(f * e) * tf]/[t(f + e) - tf]11.Capacity of the tank is , F = (f * e)/(e - f) Page 3
- 4. Solved Examples1. Two taps A and B can fill a tank in 10 hours and 15 hours and 15 hoursrespectively. If both the taps are opened together, the tank will be full in ?Ans:6hrsBasic Formula: If A can do a piece of work in x hours and B can do a piece of work in y hours. Then xyA and B together will do the work in hours x yAnswer with Explanation: Time taken by A = 10 hours Time taken by B = 15 hours 15 X 10Time taken by A and B = 15 10 15X 10 = = 6 hours. 252. To fill a cistern, pipes A, B and C take 20 minutes, 15 minute and 12 minutesrespectively. The time in minutes that the three pipes together will take to fill the cistern is:Ans:5 TCS 2008Basic Formula:A can do a piece of work in x minutesB can do a piece of work in y minutesC can do a piece of work in z minutesMinute’s work of each of the three is 1/x +1/y + 1/z Page 4
- 5. Answer with Explanation: 1 minutes work of each of the three pipes = 1/20 + 1/15 + 1/12 3 4 5 12 = = 60 60 = 1/5 = 5 minutes3. Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties thefull tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tankwill be filled?Ans;7 hrs 30 minsBasic Formula:Pipe A can fill a tank in x hours and pipe B can fill a tank in y hours and pipe C can empty itin z hours. If all the pipes are operate simultaneously,1 hours of work of each of the three pipes = 1/x +1/y - 1/zAnswer with Explanation:1 minutes work of each of the three pipes = 1/10 + 1/12 - 1/20 6 5 3 8 = = 60 60 2 = 15 = 15/2 hours = 7 ½ hour = 7 hours 30 minutes. Page 5
- 6. 4. A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. Ifthe cistern is full, then the time that the leak will take to empty it is: CAT 2007Ans:90 hrsBasic Formula: If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be xyfilled (empty) in hours x yAnswer with Explanation: Time taken by A = 9 hours Time taken by B = 10 hours 9 x10Time taken by A and B = 10 9 = 90 hours.5. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 ½hours to fill the tank. The leak can drain out of all the water of the tank in:Ans:21 hrsBasic Formula:If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled xy(empty) in hours x yAnswer with Explanation: Time taken = 3 hours Time taken = 3 ½ hours 1 3 x3 Time taken by A and B = 2 1 3 3 2 Page 6
- 7. 7 3x = 2 7 3 2 7 3x = 2 7 6 2 = 21 hours6. Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If bothare opened and A is closed after 3 minutes. How much further time would it take for B to fillthe bucket? WIPRO 2009Ans 8 min 15 secBasic Formula: Total work (to fill or empty) = I part + II part =1 Find I st part and subtract it from ‘1’ , then multiply the required section value to find the answer.Answer with Explanation:For 3 minutes (I part) 1 1 =3 12 15 15 12 = 3 15 X 12 3 = 3 = 9/20 20Remaining part = 1- 9/20 = 11/20 Page 7
- 8. Tap B fill the bucket in 11 = -15 20 = 33/4 = 8 ¼ hours = 8 hours 15 seconds.7. A tank can be filled by a tap in 20 minutes and by another tap in 60 mintues. Bothtaps are kept open for 10 mintues and then the first tap is shut off. After this, the tank will becompletely filled in:Ans:20 minBasic Formula:Total work (to fill or empty) = I part + II part =1Answer with Explanation:For 10 minutes (I part) 1 1= 10 20 60 4= 10 60= 4/6 = 2/3Remaining part= 1- ( I part)= 1-2/3= 1/3The tank will be complete by filled in (B only, after 10 minutes) = 1/3 X 60 Page 8 = 20 minutes.
- 9. 8. If two pipes function simultaneously the reservoir will be filled in 12 hours, onepipe fills the reservoir 10 hours faster than the other. How many hours it takes the secondpipe to fill the reservoir? ACCENTURE 2008Ans:30 hoursBasic Formula: xyTaken unknown value as x and use x yAnswer with Explanation:Let the reservoir be filled by forst pipe in x hours, therefore the second pipe will fill it in(x+10) hours. 1/x + 1/ x+10 = 1/12 x 10 x = 1/12 x( x 10)12 (10+2x) = x2 +10xx2 +10x – 24x – 120 = 0x2 – 14x – 120 = 0(x-20) (x+6) = 0 x = 20 (x should nor –ve) The second pipe can take (x+10) = 20 + 10 = 30 hours, to fill the reservoir.One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. Howlong will they take to fill the cistern if both the taps are opened?Ans: 6hours Page 9
- 10. Basic Formula:Pipe A can fill a tank in ‘x’ hours and pipe B can empty it in ‘y’ hours. If both the pipes xyopened together, the tank will be filled in hours. x yAnswer with Explanation: Time taken to fill the tank = 2 hours Time taken to empty the tank = 3 hours 2X 3Time taken to fill the cistern = 3 1 = 6 hours.9. 12 buckets of water fill a taken when the capacity of each bucked is 13.5 liter. Howmany buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres ?Ans:18 CTS 2007Basic Formula:Here the tank is sameNumber of buckets X capacity of bucket = Number of buckets X capacity of bucketAnswer with Explanation:The capacity of the tank is same,N1 X W1 = N2X W2 N1 = No. of Buckets W1 = Capacity of liters in the bucketsN2 = No. of Buckets W2 = Capacity of liters in the buckets = 12 X 13.5 = N2 X9 12X 13.5 = N2 = = 54/3 9 Page 10 = N2 = 18
- 11. 10. Bucket p has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill theempty drum. How many turns it will take for both the buckets p and q having each turntogether to fill the empty drum:Answer:45Basic Formula: xy x yAnswer with Explanation:Bucket P has thrice the capacity as bucket QQ= 3 PP takes 60 turnsQ takes = 180 turns 180 X 60P and Q takes = 60 180 180X 60 = 240 = 45 turns.11. Two pipes A and B fill a tank in 15 hours and 20 hours respectively while a thirdpipe c can empty the full tank in 25 hours. All the three pipes are opened in the beginning,after 10 hours, c is closed. In how much time, will the tank be full ? ans:12 hrsBasic Formula:1/x +1/y - 1/z Part I and Part II = 1Answer with Explanation:A B C Page 1115 20 -25
- 12. 1 1 1For 10 hours = 10 15 20 25 20 15 12 = 10 300 300 300 23 = 10 300 = 23/30 ( Part I)Remaining part =1- 23/30 = 7/30(A+B)’s 1 hour work = 1/15 + 1/20 = 4/60 + 3/60 = 7/60 Therefore = 7/30 X 60/7 = 2 hours Hence 10+2 = 12 hours12. Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respectivelybut a third pipe c can empty the full tank in 6 mintues. A and B are kept open for 5 minutes inthe beginning and then c is also opened. In what time is the cistern emptied …..Ans:45 mintsBasic Formula:1/x +1/y - 1/zAnswer with Explanation:A B C12 15 -6 1 1For 5 minutes = 5 12 15 Page 12
- 13. 27 = 5 180 = ¾When all the three pipes are opened = 1/12 + 1/15 – 1/6 = 15/180 + 12/180 – 30/180 = -3/180 = -1/60 (-means emptying)Empty the cistern in 1 min is 1/60Therefore ¾ will emptied in ¾ X 60 = 45 minutes.13. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for2hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hourstaken by C alone to fill the cistern is: INFOSYS 2008Answer:14Basic Formula: C’s work = (A+B+C)’s work – (A+B)’s workAnswer with Explanation:A+B+C = 1/6For 2 hours = 2 (1/6) = 1/3Remaining = 2/3(A+B)’s 7 hours work = 2/3(A+B)’s 1 hours work = 2/21C’s 1 hour work = (A+B+C)’s work – (A+B)’s work = 1/6 -2/21 = 9/126 = 1/14C alone can fill the tank in 14 hours Page 13
- 14. 14. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fillswater are the rate of 6 liters a minute. When the tank is full, the inlet is opened and due to theleak, the tank is empty in 12 hours. How many litres does the cistern hold ?Ans: 8,640Basic Formula:Work done = 1/x – 1/y Time X number of litersAnswer with Explanation: Time taken to fill the tank is 1/8 Time taken to empty the taken is 1/12 1 1 12 8Work done by the inlet in 1 hour = = 8 12 12 X 8 4 = = 1/24 12 X 8Work done by the inlet in 1 minute = 1/24 X 1/60 = 1/1440Therefore Volume = 1440 X6 liters = 8640 liters Page 14
- 15. Solved problems1.A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water atthe rate of 4 litres a minute. When the tank is full the inlet is opened and due to the leak thetank is empty in 8 hours. The capacity of the tank in litres is : Ans 5760. CAT 2010Basic Formula: Work done = 1/x – 1/y Time X number of litersAnswer with Explanation:Time taken to fill the tank is 1/6 hour (Time taken to empty = time taken to full)Time taken to empty the tank is 1/8Work done by the inlet in 1 hour = (1/6 – 1/8) 8 6 = = 2 / 48 = 1/24 6X 8For 1 minute = 1/24X1/60 = 1/1440An inlet pipe fill water at the rate of 4 liters a minute = 1440 X 4 = 5760 liters 02.A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already half-full and both tanks are opened together, the tank will be :Ans: emptied in 8 minBasic Formula:Work done = 1/x – 1/yAnswer with Explanation:Time taken to fill the tank in = 1/16 min Page 15Time taken to empty the tank in = 1/8 min
- 16. Work done by both in 1 min = (1/16 – 1/8) 8 16 = = -8 / 16X8 16 X 8 = -1/16 (-ve means empty)Now full tank will be emptied by them in 16 minHalf tank will be emptied in 8 min. 03.A cistern has two taps which fill it in 12 min and 15 min respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 mintues. How long will waste pipe take to empty the full cistern ?Ans;10 minBasic Formula:C’s work = (A+B+C)’s work – (A+B)’s workA + B = 1/x+1/yAnswer with Explanation: 27 To fill the cistern = (1/12 + 1/15) = 12 X 15 = 3/20 Work done by waste pipe in 1 min = work done by all the three taps – work done by two taps (fill) = 1/20 – 3/20 = -2/20 = -1/10 (-ve means empty) Waste pipe will empty the full cistern in 10 minutes. 04.Two pipes A and B can fill a cistern in 12 minutes and 15 mint respectively. If both the pipes are opened together, then after how much time B should be closed so that the tank is full in 9 minutes? CAT 2010 Page 16Ans 4 min
- 17. Basic Formula:Let B be closed after x minutes.I part + II part = 1I part = Cistern filled by (A+B) in x minII part = Cistern filled by A in (9-x) minutesAnswer with Explanation: 1 1 x + (9-x) X 1/12 = 1 12 16 16 12 9 x x = 1 12 X 16 12 12 28 x - x/12 = 1-9/12 12 x16 7x x = 3/12 12 x 4 12 7x – 4x = 12 3x = 12 X = 4 So, B must be closed after 4 minutes.05. A water tank is two – fifth full. Pipe A can fill a tank in 10 minutes and pipe B can emptyit in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tankcompletely?Answer : 6 minutesBasic Formula:AB/B-AAnswer with Explanation:Water level in the tank is 2/5 Page 17
- 18. 10 6 4 1Both the pipes are open = = = 10 X 6 60 15Therefore 2/5 X15 = 6 minutes06.. Pipes A and B take 20 and 30 minutes to fill a tank respectively. The 2 together will takeAnswer : 12Basic Formula:AB/A+ BAnswer with Explanation:A = 20B = 30Together = A+B/AB 20 30 = 20 X 30 50 1 = = 20 X 30 12Therefore 12 minutes.07.. 2 pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both are openedsimultaneously, how much time will be taken to fill the tank?Answer : 20 hoursBasic Formula:Time taken to fill the tank = A+B/ABAnswer with Explanation:A = 36B = 45 Page 18
- 19. AB 36 X 45 =A B 36 45 36X 45 = 81 = 20 hours 08.Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ? INFOSYS 2007Ans: 5 hoursBasic Formula:It’s an alternate hour’s problemA’s 1hour work = 1/6B’s 1 hour work = ¼A + B means 2 hours of workAnswer with Explanation: 1 1 4 6 (A+B)’s 2 hours work when opened alternately = = 6 4 24 (A+B)’s 4 hours work when opened alternately = 2 (5/12) = 5/6Remaining = 1-5/6 =1/6 It is A’s turn and 1/6 part is filled by A in 1 hour Total time taken to fill the tank = (4+1) hours = 5 hours Page 19
- 20. 9.A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipemeant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while eachof those that empty the tank can empty it in 6 hours. If all the pipes are kept open when thetank is full, it will take exactly 6 hours for the tank to empty. How many of these are fillpipes? (1) 2 (2) 4 (3) 6 (4) 5Correct Answer - (2)Solution:Let the number of fill pipes be ‘n. Therefore, there will be 8-n, waste pipes.Each of the fill pipes can fill the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8thof the tank in an hour.Hence, n fill pipes will fill n/8th of the tank in an hour.Similarly, each of the waste pipes will drain the full tank in 6 hours. That is, each of the wastepipes will drain 1/6th of the tank in an hour.Therefore, (8-n) waste pipes will drain ((8-n)/6)th of the tank in an hour.Between the fill pipes and the waste pipes, they drain the tank in 6 hours. That is, when all 8of them are opened, 1/6th of the tank gets drained in an hour.(Amount of water filled by fill pipes in 1 hour - Amount of water drained by waste pipes 1hour) = 1/6th capacity of the tank drained in 1 hour.n/8 - 8-n / 6 = -1/6 => 6n-64+8n / 48 = -1/6 => 14n-64= -8 or 14n = 56 or n=4Note: In problems pertaining to Pipes and Cisterns, as a general rule find out the amount ofthe tank that gets filled or drained by each of the pipes in unit time (say in 1 minute or 1hour).10.There are 12 pipes that are connected to a tank. Some of them are fill pipes and the othersare drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipescan drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, anempty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes? (1) 6 (2) 8 (3) 7 (4) 5 Page 20
- 21. ANS:3SolutionLet there be ‘n’ fill pipes attached to the tank.Therefore, there will be 12 - n drain pipes attached to the tankEach fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8th of thetank in an hour.Hence, n fill pipes will fill n*1/8 = n/8 th of the tank in an hour.Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain1/6 th of the tank in an hour.Hence, 12 - n drain pipes will drain(12-n) / 6 = 12-n / of the tank in an hour.When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow.Therefore, in an hour 1/24 thof the tank gets filled.Hence,n/8 - 12 - n/6 = 1/24.i.e.3n - 4(12-n) / 24 = 1/24 or 7n - 48 = 1 => 7n = 49 or n = 7.11.A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3.The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is theemptying capacity of the pump if the pump needs 12 more minutes to fill the tank than toempty it? (1) 50 m3 / min (2) 60 m3 / min (3) 45 m3 / min (4) 90 m3 /minCorrect Answer - (2)Solution:Let ‘f’ m3/min be the filling capacity of the pump. Therefore, the emptying capacity of thepump will be= (f + 10) m3 / min.The time taken to fill the tank will be = 3600 / f minutesAnd the time taken to empty the tank will be = 3600 / f+10.We know that it takes 12 more minutes to fill the tank than to empty iti.e 3600/f - 3600 / f+10 = 12 => 3600 f + 36000 - 3600 f = 12 (f2 + 10 f) Page 21
- 22. => 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.Solving for positive value of ‘f’ we get, f = 50.Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min12.Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, ittakes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tankif pipe A is shut? (1) 2 hours 30 minutes (2) 5 hours (3) 4 hours (4) 10 hoursCorrect Answer - (4)Solution:Pipe A fills the tank normally in 2 hours. Therefore, it will fill ½ of the tank in an hour.Let the leak take x hours to empty a full tank when pipe A is shut. Therefore, the leak willempty 1/4 of the tank in an hour.The net amount of water that gets filled in the tank in an hour when pipe A is open and whenthere is a leak = 1/2 -1/x of the tank. — (1)When there is a leak, the problem states that Pipe A takes two and a half hours to fill the tank.i.e. 5/2 hours. Therefore, in an hour, 5/2 th of the tank gets filled. – (2)Equating (1) and (2), we get 1/2 - 1/x =2/5=> 1/x = 1/2 - 2/5 = 1/10 => x = 10 hours.13. There are 12 pipes attached to a tank. Some of them are fill pipes and some are drainpipes. Each of the fill pipes can fill the tank in 12 hours, while each of the drain pipes willtake 24 hours to drain a full tank completely. If all the pipes are kept open when the tank wasempty, it takes 2 hours for the tank to overflow. How many of these pipes are drain pipes? (1) 6 (2) 11 (3) 4 (4) 7Correct Answer - (3) Page 22
- 23. There are 12 pipes attached to the tank. Let ‘n’ of them be fill pipes. Therefore, there will be12-n drain pipes.Each fill pipe, fills the tank in 12 hours. Therefore, 1/12th of the tank gets filled every hourby one fill pipe.‘n’ fill pipes will, therefore, fill n/12 th of the tank in an hour.Each drain pipe drains the tank in 24 hours. That is, 1/24 th of the tank gets drained by onedrain pipe every hour.12-n drain pipes, will therefore, drain 12-n / 24 th of the tank in an hour.When all the pipes are open when the tank is empty, it takes 2 hours for the tank to overflow.i.e. ½ the tank gets filled every hour.Equating the information, we get n/12 - 12-n/24 = 1/2=> 2n+n-12 / 24 = 1/2 => 3n - 12 = 12 or 3n = 24 or n = 8.Therefore, there are 8 fill pipes and (12 - 8) = 4 drain pipes.14.Pipe A can fill a tank in a hours. On account of a leak at the bottom of the tank it takesthrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty afull tank, when pipe A is kept closed? CAT 2010 (1) (3/2)a hours (2) (2/3)a (3) (4/3)a (4) (3/4)aCorrect Answer - (1)Solution:Pipe A fills the tank in a hours. Therefore, of the tank gets filled in an hour. On account ofthe leak it takes 3a hours to fill the tank. Therefore, of the tank gets filled in an hour. Let theleak at the bottom of the tank take x hours to empty the tank. Hence, 1/x of the tank getsemptied every hour.1/a - 1/x =1/3a => 1/x =1/a - 1/3a = 2/3a Page 23Hence, x = 3a/2
- 24. 15.Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. Ifboth the pipes were kept open when the tank is empty, how much time will it take for the tankto overflow?Explanatory AnswerPipe B fills the tank 5 times as fast as pipe A.Therefore, pipe B will fill the tank in one-fifth of the time that pipe A takes.Pipe B will fill the tank in = 6 minutes.In 1 minute, pipe A will fill th of the tank and pipe B will fill th of the tank.Therefore, together, the two pipes will fill th of the tank in a minuteHence, the two pipes working together will take 5 minutes to fill the tank.16.Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and Cdischarge chemical solutions P,Q and R respectively. What is the proportion of the solution Rin the liquid in the tank after 3 minutes? 5 6A. B. 11 11 7 8C. D. 11 11Answer: Option BExplanation: 1 1 1 11 11Part filled by (A + B + C) in 3 minutes = 3 + + = 3x = . 30 20 10 60 20 . Page 24
- 25. Part filled by C in 3 minutes = 3 10 3 20 6 Required ratio = x = . 10 11 1117. 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: 13 8A. 1 hours B.2 hours 17 11 9 1C. 3 hours D.4 hours 17 2Answer: Option CExplanation: 1 1 1 17Net part filled in 1 hour + - = . 5 6 12 60 60 9 The tank will be full in hours i.e., 3 hours. 17 1718.A pump can fill a tank with water in 2 hours. Because of la leak, it took 2 hours to fillthe tank. The leak can drain all the water of the tank in: 1A. 4 hours B.7 hours 3C. 8 hours D.14 hoursAnswer: Option DExplanation: 13 1Work done by the leak in 1 hour = - = . 2 7 14 Page 25
- 26. Leak will empty the tank in 14 hrs.19.Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Bothpipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:A.5 min. B.9 min.C.10 min. D.15 min.Answer: Option BExplanation:Let B be turned off after x minutes. Then,Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. 2 1 2 x + + (30 - x). = 1 75 45 75 11x (60 -2x) + =1 225 75 11x + 180 - 6x = 225. x = 9.20.A tank is filled by three pipes with uniform flow. The first two pipes operatingsimultaneously fill the tank in the same time during which the tank is filled by the third pipealone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower thanthe third pipe. The time required by the first pipe is:A.6 hours B.10 hoursC.15 hours D.30 hoursAnswer: Option CExplanation:Suppose, first pipe alone takes x hours to fill the tank . Page 26
- 27. Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank. 1 1 1 + = x (x - 5) (x - 9) x-5+x 1 = x(x - 5) (x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0(x - 15)(x - 3) = 0 x = 15. [neglecting x = 3]21.Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3gallons per minute. All the three pipes working together can fill the tank in 15 minutes. Thecapacity of the tank is:A.60 gallons B.100 gallonsC.120 gallons D.180 gallonsAnswer: Option CExplanation: 1 1 1Work done by the waste pipe in 1 minute = - + 15 20 24 1 11 = - 15 120 1 =- . [-ve sign means emptying] 40 1 Volume of part = 3 gallons. 40 Page 27Volume of whole = (3 x 40) gallons = 120 gallons.
- 28. 22.A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B andB is twice as fast as A. How much time will pipe A alone take to fill the tank?A.20 hours B.25 hoursC.35 hours D.Cannot be determinedE. None of theseAnswer: Option CExplanation:Suppose pipe A alone takes x hours to fill the tank. x xThen, pipes B and C will take and hours respectively to fill the tank. 2 4 1 2 4 1 + + = x x x 5 7 1 = x 5 x = 35 hrs.23.Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately,then B would have taken 6 hours more than A to fill the cistern. How much time will be takenby A to fill the cistern separately?A.1 hour B.2 hoursC.6 hours D.8 hoursAnswer: Option CExplanation:Let the cistern be filled by pipe A alone in x hours.Then, pipe B will fill it in (x + 6) hours. 1+ 1 =1 Page 28
- 29. x (x + 6) 4 x+6+x 1 = x(x + 6) 4 x2 - 2x - 24 = 0 (x -6)(x + 4) = 0 x = 6. [neglecting the negative value of x]24. 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? A.12 min B.15 min C.25 min D.50 minAnswer: Option AExplanation: 1Part filled by A in 1 min = . 20 1Part filled by B in 1 min = . 30 1 1 1Part filled by (A + B) in 1 min = + = . 20 30 12 Both pipes can fill the tank in 12 minutes.25.. 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. Page 29
- 30. Answer: Option DExplanation: 1 1 7Part filled in 4 minutes = 4 + = . 15 20 15 7 8Remaining part = 1 - = . 15 15 1Part filled by B in 1 minute = 20 1 8 : :: 1 : x 20 15 8 2x= x 1 x 20 = 10 min = 10 min. 40 sec. 15 3 The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.26. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:A. 81 min. B.108 min.C. 144 min. D.192 min.Answer: Option CExplanation:Let the slower pipe alone fill the tank in x minutes. xThen, faster pipe will fill it in minutes. 3 1 3 1 + = x x 36 Page 30
- 31. 4 1 = x 36 x = 144 min.27. A large tanker can be filled by two pipes A and B in 60 minutes 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. 15 min B.20 minC. 27.5 min D.30 minAnswer: Option DExplanation: 1 1 1Part filled by (A + B) in 1 minute = + = . 60 40 24Suppose the tank is filled in x minutes. x 1 1Then, + =1 2 24 40 x 1 x =1 2 15 x = 30 min.28. 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 minC.4 hrs D.4 hrs 15 minAnswer: Option BExplanation:Time taken by one tap to fill half of the tank = 3 hrs. Page 31
- 32. 1 2Part filled by the four taps in 1 hour = 4 x = . 6 3 1 1Remaining part = 1 - = . 2 2 21 : :: 1 : x 32 1 3 3 x= x 1 x = hours i.e., 45 mins. 2 2 4So, total time taken = 3 hrs. 45 mins.29. 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 and C are open for one hour each alternately, the tank will be full in: 2A.6 hours B.6 hours 3 1C.7 hours D.7 hours 2Answer: Option CExplanation: 1 1 9 3(A + B)s 1 hours work = + = = . 12 15 60 20 1 1 8 2(A + C)s hours work = + = = . 12 20 60 15 3 2 17Part filled in 2 hrs = + = . 20 15 60 Page 32
- 33. 17 17Part filled in 6 hrs = 3 x = . 60 20 17 3Remaining part = 1 - = . 20 20 3Now, it is the turn of A and B and part is filled by A and B in 1 hour. 20 Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.30. 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.12C. 14 D.16Answer: Option CExplanation: 2 1Part filled in 2 hours = = 6 3 1 2Remaining part = 1 - = . 3 3 2 (A + B)s 7 hours work = 3 2(A + B)s 1 hours work = 21 Cs 1 hours work = { (A + B + C)s 1 hours work } - { (A + B)s 1 hours work } 1 2 1 = - = 6 21 14 Page 33
- 34. C alone can fill the tank in 14 hours.31. If both the pipes are opened, how many hours will be taken to fill the tank? I. The capacity of the tank is 400 litres. II. The pipe A fills the tank in 4 hours. III. The pipe B fills the tank in 6 hours.A. Only I and IIB. Only II and IIIC. All I, II and IIID. Any two of the threeE. Even with all the three statements, answer cannot be given.Answer: Option BExplanation: 1 II. Part of the tank filled by A in 1 hour = 4 1III. Part of the tank filled by B in 1 hour = 6 1 1 5(A + B)s 1 hours work = + = 4 6 12 12 A and B will fill the tank in hrs = 2 hrs 24 min. 5So, II and III are needed. Correct answer is (B).32. How much time will the leak take to empty the full cistern? I. The cistern is normally filled in 9 hours. II. It takes one hour more than the usual time to fill the cistern because of la leak in the bottom.A. I alone sufficient while II alone not sufficient to answerB. II alone sufficient while I alone not sufficient to answer Page 34
- 35. C. Either I or II alone sufficient to answerD. Both I and II are not sufficient to answerE. Both I and II are necessary to answerAnswer: Option EExplanation:I. Time taken to fill the cistern without leak = 9 hours. 1Part of cistern filled without leak in 1 hour = 9II. Time taken to fill the cistern in presence of leak = 10 hours. 1Net filling in 1 hour = 10 1 1 1Work done by leak in 1 hour = - = 9 10 90 Leak will empty the full cistern in 90 hours.Clearly, both I and II are necessary to answer the question. Correct answer is (E).33.How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B areopened simultaneously? I. A can fill the tank in 16 minutes. II. B can empty the full tank in 8 minutes. A.I alone sufficient while II alone not sufficient to answer B.II alone sufficient while I alone not sufficient to answer C.Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E.Both I and II are necessary to answerAnswer: Option EExplanation: Page 35
- 36. 1I. As 1 minutes filling work = 16 1II. Bs 1 minutes filling work = 8 1 1 1(A + B)s 1 minutes emptying work = - = 8 16 16 Tank will be emptied in 16 minutes.Thus, both I and II are necessary to answer the question. Correct answer is (E).34.Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe Bfills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains thetank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed andpipe B is kept open for a minute and then closed and then pipe C is kept open for a minuteand then closed and the cycle repeated, how long will it take for the empty tank to overflow?(1) 42 minutes(2) 14 minutes(3) 39 minutes(4) 40 minutes 33 seconds(5) None of theseCorrect Choice - (5). Correct Answer is None of theseExplanatory AnswerPipe A fills the tank at the rate of 40 litres a minute. Pipe B at the rate of 30 litres a minuteand Pipe C drains the tank at the rate of 20 litres a minute.If each of them is kept open for a minute in the order A-B-C, the tank will have 50 litres ofwater at the end of 3 minutes.After 13 such cycles, the tank will have 13 * 50 = 650 litres of water.It will take 13 * 3 = 39 minutes for the 13 cycles to be over.At the end of the 39th minute, Pipe C will be closed and Pipe A will be opened. It will add 40litres to the tank.Therefore, at the end of the 40th minute, the tank will have 650 + 40 = 690 litres of water.At the end of the 40th minute, Pipe A will be closed and Pipe B will be opened. It will add 30litres of water in a minute.Therefore, at the end of the 41st minute, the tank will have 690 + 30 = 720 litres of water.But then at 700 litres, the tank will overflow. Therefore, Pipe B need not be kept open for afull minute at the end of 40 minutes. Page 36Pipe B needs to add 10 more litres of water at the end of 40 minutes. It will take 1/3rd of a
- 37. minute to fill 10 litres of water.Therefore, the total time taken for the tank to overflow = 40 minutes + 1/3 of a minuteor 40 minutes 20 seconds.35.A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3.The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is theemptying capacity of the pump if the pump needs 12 more minutes to fill the tank than toempty it? 1. 50 m3 / min 2. 60 m3 / min 3. 45 m3 / min 4. 90 m3 /min 5. 72 m3 /minCorrect Choice - (2). Correct Answer is 60 m3 / minExplanatory AnswerLet f m3/min be the filling capacity of the pump.Therefore, the emptying capacity of the pump will be = (f + 10 ) m3 / min.The time taken to fill the tank will be = minutesAnd the time taken to empty the tank will be = .We know that it takes 12 more minutes to fill the tank than to empty iti.e = 12=> 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.Solving for positive value of f we get, f = 50.Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min Page 37
- 38. 36.There are three taps A, B and C in a container. Tap A and B can fill the container in 15and 10 minutes respectively, if they are working alone. Tap C can empty it in 12 minutes ifit is working alone. Initially all the Taps are closed. Tap A is opened alone for 3 minutes.Now A is closed and B is opened alone for 2 minutes. Now B is closed and C is openedalone for 5 minutes. Finally all the three taps are opened together. How long will it take tofill the tank? 10 minutes 12 minutes Tank Cannot be filled None of theseAnswer :12 minutesSolution (Fast Approach)Part 1 Tap A alone can fill 100% of the container in 15 min.Its opened for 3 minutes. Hence it fills (3/15)x100 = 20% of the conatainer In the same way in 2 minute B can fill (2/10)x100 = 20%. Now container is 40% full Now Tap C is opened for 5 min. It can empty (5/12)x100 = 41.67% of the container in 5min. Only 40% of the container is filled, hence C will completely empty the container.Part 2 In 1 min A, B and C combined can fill (1/15 + 1/10 - 1/12) = 1/12 portion of the container Hence 1 portion (Full) can be filled in 1/(1/12) = 12 minutes37. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipesare opened simultaneously, how much time will be taken to fill the tank?Sol. Part filled by A In 1 hour = 1/36Part filled by B in 1 hour = 1/45Part filled by (A + B) In 1 hour = [1/36 + 1/45] = 9/180 = 1/20Hence, both the pipes together will fill the tank in 20 hours.38. A pipe can fill a tank in 16 hours. Due to a leak in the bottom,it is filled in 24 hours. If thetank is full, how much time will the leak take to empty it ? Page 38
- 39. Sol. Work done by the leak in 1 hour = [ 1/16 – 1/24 ]=1/48:. Leak will empty the full cistern in 48 hours.39. A cistern is filled by pipe A in 10 hours and the full cistern can be leaked out by anexhaust pipe B in 12 hours. If both the pipes are opened, in what time the cistern is full?Sol. Work done by the inlet in 1 hour: = 1/10Work done by the outlet in 1 hour = 1/12Net part filled in 1 hour = [ 1/10 – 1/12 ] = 1/60The cistern will be full in 60 hours.40. Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are openedsimultaneously and it is found that due to leakage in the bottom, 32 minutes extra are takenfor the cistern to be filled up. When the cistern is full in what time will the leak empty it ?Sol. Work done by .the two pipes in 1 hour = [ 1/14 + 1/16 ] = 15/112... Time taken by these pipes to fill the tank = 112/15 hours = (7 hrs. 28 min.)Due to leakage, time taken = (7 hrs 28 min.) + 32 min. = 8 hrsWork done by ( two pipes + leak) in 1 hour = 1/8Work done by the leak m 1 hour = [ 15/112 – 1/8 ] = 1/112Leak will empty the full cistern in 112 hours41. Pipes A and B can fill a tank in 20 hours and 30 hours respectively and pipe C can emptythe full tank in 40 hours. If all the pipes are opened together, how much time will be neededto make the tank full ?Sol. Net part filled m 1 hour = [1/20 + 1/30 – 1 /40] = 7/120 The tank will be full in 120/7 = 17 ½42. Two pipes A and B can frll a tank in 24 min. and 32 min. respectively. If both the pipesare opened simultaneously, after how much time B should be closed so that the tank is full in18 minutes?Sol. Let B be closed after x minutes. Then,part filled by (A + B) in x min. + part filled by A in (18 - x) min. = 1.X {1/24 + 1/32] + (18 – x) X 1/24 = 1 or 7x/96 + (18 – x)/24 = 17x + 4(18 –x) = 96 or x=8Hence, B must be closed after 8 minutes43. Two pipes A and B can fill a tank in 36 min. and 4S min. respectively. A water pipe Ccan empty the tank in 30 min. First A and B are opened. After 7 minutes, C is opened. In howmuch time, the tank Is full ?Sol. Part filled in 7 min = 7[ 1/36 + 1/45] = 7/20 Page 39
- 40. Remaining part = [ 1- 7/20] = 13/20Net part filled in 1 min. When A,B and C are opened= [ 1/36 + 1/45 + 1/30 ] = 1/60Now, 1/60 part is filled in 1 min.13/20 part is filled in [60x13/20] = 39 minTotal time taken to fill the tank = (39 + 7) min. = 46 min.44.There are 12 pipes that are connected to a tank. Some of them are fill pipes and the othersare drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipescan drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, anempty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?(1) 6(2) 8(3) 7(4) 5(5) 4Correct Choice - (3). Correct Answer is 7 pipesExplanatory Answer Let there be n fill pipes attached to the tank. Therefore, there will be 12 - n drain pipes attached to the tank Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill th of the tank in an hour. Hence, n fill pipes will fill of the tank in an hour. Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain th of the tank in an hour. Page 40
- 41. Hence, (12 - n) drain pipes will drain th of the tank in an hour. When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow. Therefore, in an hour th of the tank gets filled. Hence, . i.e. or 7n - 48 = 1 => 7n = 49 or n = 7.45. Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept openthroughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes afterpipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equalshare of the tank. Furthermore, it is known that if pipe A and B are kept open continuously,the tank would be filled completely in t minutes. Find t?A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill theentire tank in 3t minutes.A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.A and B together can fill 1/t of the tank in a minute. A alone can fill 1/3t of the tank in aminute. So, in a minute, B can fill 1/t - 1/3t = 2/3t. Or, B takes 3t/2 minutes to fill an entiretankTo fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.t/2 = t - 10, t = 20 minutes.A takes 60 mins to fill the entire tank, B takes 30 minutes to fill the entire tank. A is keptopen for all 20 minutes. B is kept open for 10 minutes.C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tankin 24 minutes. Page 41
- 42. 46.Pipe A fills a tank at the rate of 100lit/min, Pipe B fills at the rate of 25 lit/min, pipe Cdrains at the rate of 50 lit/min. The three pipes are kept open for one minute each, one afterthe other. If the capacity of the tank is 7000 liters, how long will it take to fill the tank ifi) A is kept open first, followed by B and then CEach cycle of 3 minutes, 75 liters get filled. 100 + 25 - 50. So, after 3 minutes the tank wouldhave 75 liters6 mins - 150 liters9 mins - 225 liters30 mins - 750 liters270 mins - 6750 liters273 mins - 6825 liters279 mins - 6975 litersIn the 280th minute, pipe A would be open and it would fill the remaining 25 liters in 15seconds. So, it would take 279 mins and 15 seconds to fill the tank.The most important thing in these type of questions is to think in terms of cycles till we reachclose to the required target and then think in simple steps.ii) B first, followed by A, and then CEach cycle of 3 minutes, 75 liters get filled. 25 + 100 - 50. So, after 3 minutes the tank wouldhave 75 liters6 mins - 150 liters9 mins - 225 liters30 mins - 750 liters270 mins - 6750 liters273 mins - 6825 liters279 mins - 6975 litersIn the 280th minute, pipe B would be open and it would fill the remaining 25 liters in oneminutes. So, it would take 280 mins. Page 42
- 43. iii) B first, followed by C, and then AIn this case also, Each cycle of 3 minutes, 75 liters get filled. 25 -50 + 100. But there is asmall catch here. In the first set of 3 minutes, we would fill up to about 100 liters. After 1minute, we would be at 25 liters, after 2 minutes, we would be at 0 liters and in the thirdminute, the tank would be 100 liters full.6 mins - 170 liters9 mins - 250 liters30 mins - 775 liters270 mins - 6775 liters273 mins - 6850 liters276 mins - 6925 liters279 minutes - 7000 litersSo, it would take 279 mins and 15 seconds to fill the tank.The mOst Important thing in these type of questions is to think in terms of cycles till wereach close to the required target and then think in simple steps.47. A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a systemof n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, whichof the following are possible values of n (More than one option could be correct)?1) 32 2) 54 3) 29 4) 403 fill pipes cancel out 2 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5hours. so the answer has to be 5k + 4. Both 54 and 29 are possible. Page 43
- 44. PROBLEMS FOR THE TEST1.Two taps A and B can fill a tank in 10 hours and 15 hours and 15 hours respectively. Ifboth the taps are opened together, the tank will be full in ? Ans:6hrs2.To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The timein minutes that the three pipes together will take to fill the cistern is Ans:53.Two pipes can fill a tank in 10 hours and 12 hours resp. while third pipe empties the fulltank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank willbe filled? Ans;7 hrs 30 mins4.A cistern can be filled in 9 hours but it takes 10 hours due to a leak in its bottom. If thecistern is full, then the time that the leak will take to empty it is Ans:90 hrs5.an electric pump can fill a tank in 3 horus. Because of a leak in the tank, it took 3 ½ hoursto fill the tank. The leak can drain out of all the water of the tank in Ans:21 hrs6.Taps A and B can fill a bucket in 12 minutes and 15 minutes resp. If both are opened and Ais closed after 3 minutes. How much further time would it take for B to fill the bucket? Ans 8 min 15 sec7.A tank can be filled by a tap in 20 minutes and by another rtap in 60 mintues. Both taps arekept open for 10 mintues and then the first tap is shut off. After this, the tank will becompletely filled in Ans:20 min8.If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipe fillsthe reservoir 10 hours faster than the other. How many hours it takes the second pipe to fillthe reservoir? Ans:30 hours Page 44
- 45. 9.One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. Howlong will they take to fill the cistern if both the taps are opened? Ans: 6hours10.12 buckets of water fill a taken when the capacity of each bucked is 13.5 liter. How manybuckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres ? Ans:1811.Bucket p has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill theempty drum. How many turns it will take for both the buckets p and q having each turntogether to fill the empty drum ans:4512.Two pipes A and B fill a tank in 15 hours and 20 hours respectively while a third pipe ccan empty the full tank in 25 hours. All the three pipes are opened in the beginning, after 10horus, c is closed. In how much time, will the tank be full ? ans:12 hrs13.Two pipes A and B and can fill a cistern in 12 minutes and 15 minutes respt but a thirdpipe c can empty the full tank in 6 mintues. A and B are kept open for 5 minutes in thebeginning and then c is also opened. In what time is the cistern emptied ….. Ans:45 mints14.Three pipes A,B and C can fill a tank in 6 hours. After working at it together for 2hours, Cis closed and A and B can fill the remaining part in 7 hours. The number of hours taken by Calone to fill the cistern is ans:1415.A leak in the bottom of atank can empty the full tank in 8 hours. An inlet pipe fills waterare the rate of 6 literes a minute. When the tank is full, the inlet is opened and due to the leak,the tank is empty in 12 hours. How many litres does the cistern hold ? Ans: 8,64016.A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills waterat the rate of 4 liters a minute. When the tank is full the inlet is opened and due to the leak thetank is empty in 8 hours. The capacity of the tank (in litters is : Ans 5760.17.A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank isalready half-full and both tansk are opened together, the tank will be : Page 45
- 46. ans:emptied in 8 min18.A cistern has two taps which fill it in 12 min and 15 min resp. There is also a waste pipe inthe cistern. When all the three are opened, the empty cistern is full in 20 minutes. How longwill waste pipe take to empty the full cistern ? Ans;10 min19.Two pipes A and B can fill a cistern in 12 minutes and 15 mint resp. If both the pipes areopened together, then after how much time B should be closed so that the tank is full in 9minutes? Ans 4 min20.Two pipes A and B can fill a tank in 6 hours and 4 hours resp. If they are opened onalternate hours and if pipe A is opened first, in how many hours, the tank shall be full ? Ans: 5 hours21.Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipesare open,in how many hours will the tank be filled ? Ans: = (1/5 + 1/6 + 1/30)part filled by (A+B+C) in 1 hour ‹=› 1/3.All the three pipes together will fill the tank in 3 hours.22.A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fillthe tank. The leak can drain all the water of the tank in A. 5 hours B. 7 hours C. 8 hours D. 14 hoursAns:Leak will empty the tank in 14 hours23.Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3gallons per minute. All the three pipes working together can fill the tank in 15 minutes. Thecapacity of the tank is A. 60 gallons B. 80 gallons C. 120 gallons D. 160 gallonsAns:Work done by the waste pipe in 1minute = 1/15 - (1/20+1/24) Page 46
- 47. = (1/15 - 11/20) [ - ve sigh means = - 1/40 emptying]Volume of 1/40 part = 3 gallons.Volume of Whole = (3×40) =120 gallons.24.Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties thefull tank in 20 hours.If all the three pipes operate simultaneously, in how much time will the tankbe filled? A. 7 hrs 30 min B. 7 hrs 45 min C. 8 hrs 30 min D. 8 hrs 45 minNet apart filled in 1 hour = (1/10+1/12-1/20) = 8/60 = 2/15.Therefore the tank will be full in 15/2 hours ‹=› 7 hrs 30 min.BANK EXAM QUESTIONS25 A cistern can be filled by pipe A and B in 12 minutes and 10 minutes respectively. Thefull tank can be emptied by a third pipe C in 8 minutes only. If all the taps be turned on at thesame time, the cistern will be full in how much time?Ans:17(1/7) Minutes26 Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. If both the pipesopen together how much time will it take to fill the tank?Ans:6 Hours27. Two pipes A and B can fill a tank in 60 minutes. If pipe A alone can fill it in 75 minutes.How much time will the pipe B take to fill the tank alone?Ans:300 Minutes28. Three pipes A, B and C can fill a tank in 30 hours, 20 hours and 10 hours respectively. Ifall the pipes open together how much time is required to make the tank full?Ans:5 (5/11) Hours Page 47
- 48. 29. Three pipes A, B and C together can fill a tank in 15 minutes. One of the pipes can fill itin 45 minutes and another in 30 minutes. How much time is taken by the third pipe alone tomake the tank full?Ans:90 Minutes30. A cistern can be filled by pipe A and B in 40 minutes and 60 minutes respectively. Thereis also an outlet C. If all the taps are open together the tank is full in 2 hours. How much timeis taken by C to empty the full tank?Ans:30 Minutes31. A cistern can be filled by pipe A and B in 30 minutes and 45 minutes respectively. Thereis also an outlet C. If all the taps are open together the tank is full in 1 hour and 15 minutes.How much time is taken by C to empty the full tank?Ans:23 (13/19) Minutes32. Pipe A can fill the tank in 12 minutes and pipe B can empty it in 8 minutes. If 3/4th part ofthe tank is already full and both the pipes are open together. In much time both the pipesempty the tank?Ans:18 Minutes33.A pipe can fill a tank in 40 minutes. Due to the leakage in the bottom it is filled in 50hours. If the tank is full, how much time will the leak take to empty it?Ans:200 Minutes34.P, Q and R are three pipes connected to a tank. P and Q together fill the tank in 4 hours. Rand Q together fill the tank in 6 hours. P and R together fill the tank in 5 hours. In how muchtime will P, Q and R fill the tank together?Ans:3(9/37) Hours35. Two pipes A and B can fill a tank in 25 minutes and 35 minutes respectively. But a thirdpipe C can empty it in 10 minutes. The first two pipes are kept open for 5 minutes in thebeginning and then the third pipe is also opened. In what time is the cistern emptied?Ans:10(10/11) Hours36. A cistern can be filled by pipe A and B in 25 hours and 30 hours respectively. There isalso an outlet C which can empty it in 40 hours. If all the taps are open together. After 5minutes pipe C must be turned off. In how much time the cistern is full?Ans:10(15/44) Hours37. A tank has a leak which would empty it in 16 hours. A tap is turned on which admits 12liter a minute into the tank and it is now emptied in 24 hours. How many liters does the tankhold?Ans:34560 Liters Page 48
- 49. 38.Two pipes A and B can fill a tank in 12 minutes and 16 minutes respectively. If both thepipes open together after how much time should be B closed so, that the tank is full in 9minutes?Ans:4 Hours39.Two pipes A and B can fill a tank in 10 hours and 12 hours respectively. B is open for 2hours in the beginning, and then B is closed. In how much time A fill the remaining tank?Ans:8(1/3) Hours40.Two pipes A and B can fill a tank in 50 minutes and 60 minutes respectively. If both thepipes open together for 10 minutes, then B is closed. In how much time A fill the remainingtank?Ans:38 Minutes Page 49
- 50. 25.A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills waterat the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak,the tank is empty in 12 hours. How many litres does the cistern hold ? A. 7580 B. 7960 C. 8290 D. 8640Ans: = (1/8 - 1/12)Work done by the inlet in 1 hour = 1/24. = (1/24 × 1/60)Work done by the inlet in 1 min. = 1/1440.Volume of 1/1440 part = 6 litres. = (1440×6)Therefore, Volume of whole ‹=› 8640 litres. Page 50

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