Chapter 24 Pipes and Cisterns Problems on Pipes and Cisterns are based on the basic concept of time and work. Pipes are connected to a tank or cistern and are used to fill or empty the tank or cistern. In pipe and cistern, the work is done in form of filling or emptying a cistern/tank. Inlet pipe It fills a tank/cistern/reservoir. Outlet pipe It empties a tank/cistern/reservoir. Important Points
Ex. 2 If a pipe can fill a tank in 2 h and another pipe can fill the same tank in 6 h, then what part of a tank will be filled by both the pipes in 1 h, if they are opened simultaneously? Ex. 3 If a pipe can fill a tank in 5 h and an another pipe can empty the tank in 10 h, then part fill by both pipes in 1 h, if both pipes are open simultaneonsly.
Fast Track Techniques to solve the QUESTIONS If a pipe can fill/empty a tank in 'm' h and an another pipe can fill/empty the same tank in 'n' h, then (i) If both pipes either fills or empties the tank, then the time taken to fill or emotv the (ii) If first pipe fills the tank and second pipe empties the tank, then the time taken to (iii) if first pipe fills the tank and second pipe empties the tank, then the time taken to Ex. 4 Two pipes A and B can fill a tank in 18 h and 12 h, respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Ex. 5 A pipe can fill a tank in 5 h, while another pipe can empty it in 6 h. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? Ex. 6 A pipe can fill a tank in 10 h. Due to a leak in the bottom, it fills the tank in 20 h. If the tank is full, how much time will the leak take to empty it?
If any one of the three pipes is used to empty the tank, then time taken by that particular pipe will be negative (-ve). Suppose, 3rd pipe is used to empty the tank. Then, the above formulae takes the form as Ex. 7 Three pipes m, n and p can fill a tank separately in 4, 5 and 10 h, respectively. Find the time taken by all the three pipes to fill the tank when the pipes are opened together.
Ex. 8 Pipe A can fill a tank in 20 h while pipe B alone can fill it in 10 h and pipe C can empty the full tank in 30 h. If all the pipes are opened together, how much time will be needed to make the tank full? Sol. Part filled by pipe A alone in 1 h = — 20 Part rilled by pipe B alone in 1 h = — 10 Part emptied by pipe C alone in 1 h = — 30 Net part filled by (A + B + C) in 1 h = f — + — - — | V ^ l20 10 30j Two pipes A and B together can fill a tank in time t. If time taken by/* alone is more than t by a and time taken by B alone is more than t by b, then t = 4ab.
Ex. 9 Two pipes A and B are opened together to fill a tank. Both the pipes fill the tank in time t. If A separately takes 4 min more time than t to fill the tank and B takes 64 min more time than t to fill the tank, find the value of t. A full tank get emptied in 'a' h due to presence of a leak in it. If a tap which fills it at a rate of 'b' L/h, is opened, then it get emptied in 'c' h. Ex. 10 A full tank get emptied in 6 min due to presence of an orifice in it. On opening a tap which can fill the tank at the rate of 8 L/min, the tank get emptied in 10 min. find the capacity of tank. If two taps A and B, which can fill a tank, such that efficiency of A is n times of B and takes t min less/more than B to fill the tank, then Ex. 11 If tap A can fill a tank 3 times faster than tap B and takes 28 min less than tap B to fill the tank. If both the taps are opened simultaneously, then find the time taken to fill the tank.
Two pipes A and B can fill a tank in x min and y min, respectively. If both the nines are onened simultaneously, then the time after which nine S Ex. 12 Two pipes A and B can fill a tank in 12 and 16 min, respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 9 min?
Fast Track Practice Exercise© Base Level Questions 1. If a pipe fills a tank in 6 h, then what part of the tank will the pipe fill in 1 h? 2. An outlet pipe can empty a cistern in 30 min, then what part of the cistern will it empty in lmin? 3. An inlet pipe fills 1/8 part of a tank in 1 h. How much time will the pipe take to fill the empty tank? (a) 4 h (b) 2 h (c) 6 h (d) 8 h (e) None of the above 4. An outlet pipe can empty a cistern in 3 h. In what time will the pipe empty two-third part of the cistern? (a) 4 h (b) 2 h (c) 3 h (d) 5 h (e) None of the above 5. Two pipes A and B can fill a tank in 18 and 6 h, respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? [Bank Clerks 2008] 6. There are two tanks A and B to fill up a water tank. The tank can be filled in 40 min, if both taps are on. The same tank can be filled in 60 min, if tap A alone is on. How much time will tap B alone take, to fill up the same tank? [CDS 2012] (a) 64 min (b) 80 min
(c) 96 min (d) 120 min 7. A cistern can be filled up in 4 h by an inlet A. An outlet B can empty the cistern in 8 h. If both A and B are opened simultaneously, then after how much time will the cistern get filled? [Bank Clerks 2009] (a) 5 h (b) 7 h (c) 8 h (d) 6 h (e) None of the above 8. A pipe can fill a tank in 20 h. Due to a leak in the bottom, it is filled in 40 h. If the tank is full, how much time will the leak take to empty it? [CDS 2013] (a) 40 h (b) 30 h (c) 50 h (d) 30 h 9. A pipe can fill a tank in 10 h, while an another pipe can empty it in 6 h. Find the time taken to empty the tank, when both the pipes are opened up simultaneously. [Bank Clerks 2010] (a) 11 h (b) 15 h (c) 18 h (d) 16 h (e) None of the above 10. Three pipes A, B and C can fill a tank separately in 8 h, 10 h and 20h, respectively. Find the time taken by all the three pipes to fill the tank when the pipes are opened together. 11. Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in 3 and 4 h, respectively. The full cistern is emptied by the third tap in 5 h. If all three taps are opened simultaneously, the empty cistern will be filled up in [SSC CCL 2013] 12. Pipe A can fill a tank in 30 min, while pipe B can fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, how much time will be needed to make the tank full? [Hotel Mgmt. 2010]
13. Pipes A and B can fill a tank in 5 and 6 h, respectively. Pipe C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled un? fBank PO 2007] 14. Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it? [SSC CGL 2010] (a) 16 h (b) 20 h (c) 32 h (d) 40 h 15. A tap can fill an empty tank in 12 h and a leakage can empty the tank in 20 h. If tap and leakage both work together, then how long will it take to fill the tank? [Bank Clerks 2010] (a) 25 h (b) 40 h (c) 30 h (d) 35 h (e) None of the above 16. Three taps A, B and C together can fill an empty cistern in 10 min. The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it? [SSC CPO 2010] (a) 16 min (b) 24 min (c) 32 min (d) 40 min 17. Two pipes A and B can fill a tank in 1 h and 75 min, respectively. There is also an outlet C. If all the three pipes are opened together. The tank is full in 50 min. How much time will be taken by C to empty the full tank? (a) 100 min (b) 150 min (c) 200 min (d) 125 min (e) None of the above 18. A tank has a leak which would empty it in 8 h. A tap is turned on which admits 3 L a min into the tank and it is now emptied in 12 h. How many litres does the tank hold? (a) 4320 L (b) 4000 L
(c) 2250 L (d) 4120 L 19. A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 h, B and C together fill the tank in 10 h and A and C together fill the tank in 12 h. In how much time A, B and C fill up the tank together? 20. Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill? [SSC CGL 2013] 21. Two pipes A and B are opened together to fill a tank. Both pipes fill the tank in a certain time. If A separately takes 16 min more than the time taken by (A + B) and B takes 9 min more than the time taken by (A + B). Find the time taken by A and B to fill the tank when both the pipes are opened together. (a) 10 min (b) 12 min (c) 15 min (d) 8 min (e) None of the above 22. There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank? [SSC CGL 2007] (a) 3 h (b) 4 h (c) 5 h (d) 6 h 23. Two pipes can fill a tank in 20 and 24 min, respectively and a waste pipe can empty 6 gallon per min. All the three pipes working together can fill the tank in 15 min. Find the capacity of the tank. (a) 210 gallon (b) 50 gallon (c) 150 gallon (d) 240 gallon
(e) None of the above 24. Inlet A is four times faster than inlet B to fill a tank. If A alone can fill it in 15 min, how long will it take if both the pipes are opened together? (a) 10 min (b) 12 min (c) 15 min (d) 14 min (e) None of the above 25. There are two inlets A and B connected to a tank. A and B can fill the tank in 16 h and 10 h, respectively. If both the pipes are opened alternately for 1 h, starting from A, then how much time will the tank take to be filled? 26. Two pipes X and Y can fill a cistern in 6 and 7 min, respectively. Starting with pipe X, both the pipes are opened alternately, each for 1 min. In what time will they fill the cistern? Exercise © Higher Skill Level Questions 1. A tap having diameter 'd' can empty a tank in 40 min. How long another tap having diameter '2d' take to empty the same tank? (a) 5 min (b) 20 min (c) 10 min (d) 40 min (e) 80 min
2. Two pipes can fill a cistern in 14 and 16 h, respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, it took 92 min more to fill the cistern. When the cistern is full, in what time will the leak empty it? 3. Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed so that the tank is full in 9 min? (a) 40 min (b) 30 min (c) 10 min (d) 20 min (e) None of the above 4. Two pipes A and B can fill a cistern in 15 and 20 min, respectively. Both the pipes are opened together, but after 2 min, pipe A is turned off. What is the total time required to fill the tank? 5. A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min, but a third pipe can empty it in 6 min. The first two pipes are kept open for 5 min in the beginning and then the third pipe is also opened. Time taken to empty the cistern is [SSC CCL (Mains) 2013] (a) 38 min (b) 22 min (c) 42 min (d) 45 min 6. A tank can be filled by a tap in 20 min and by another tap in 60 min. Both the taps are kept open for 5 min and then the 1st tap is shut off. After this, how much time the tank will be completely filled? (a) 20 min (b) 30 min (c) 45 min (d) 40 min
(e) None of the above 7. A cistern has three pipes A, B and C. Pipes A and B can fill it in 3 and 4 h, respectively, while pipe C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3:00 pm, 4:00 pm and 5:00 pm, respectively, at what time will the cistern be empty? [SSC (10+2) 2007] (a) 6:15 pm (b) 7:12 pm (c) 8:12 pm (d) 8:35 pm 8. If two pipes function together, the tank will be filled in 12 h. One pipe fills the tank in 10 h faster than the other. How many hours does the faster pipe take to fill up the tank? (a) 20 h (b) 60 h (c) 15 h (d) 25 h (e) None of the above 9. A pipe P can fill a tank in 12 min and another pipe R can fill it in 15 min. But, the 3rd pipe M can empty it in 6 min. The 1st two pipes P and R are kept open for double the 2.5 min in the beginning and then the 3rd pipe is also opened. In what time is the tank emptied? (a) 30 min (b) 25 min (c) 45 min (d) 35 min (e) None of the above 10. Three pipes A, B and C can fill a tank in 30 min, 20 min and 10 min, respectively. When the tank is empty, all the three pipes are opened. If A, B and C discharge chemical solutions P, Q and R respectively, then the part of solution R in the liquid in the tank after 3 min is [SSC (10+2) 2013] 11. There are 7 pipes attached with a tank out of which some are inlets and some are outlets. Every inlet can fill the tank in 10 h and every outlet can empty the tank in 15 h. When all the pipes are opened simultaneously, the tank is filled
(a) 5, 2 (b) 6, 1 (c) 4, 3 (d) 3, 4 (e) None of the above 12. Capacity of tap B is 80% more than that of A. If both the taps are opened simultaneously, they take 45 h to fill the tank. How long will B take to fill the tank alone? {a) 72 h (b) 48 h (c) 66 h (d) 70 h (e) None of the above 13. Three taps A, B and C fill a tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the tank? (a) 1 min (b) 2 min (c) 3 min (d) 4 min (e) None of the above 14. Taps A, B and C are attached with a tank and velocity of water coming through them are 42 L/h, 56 L/h and 48 L/h, respectively. A and B are inlets and C is outlet. If all the taps are opened simultaneously, tank is filled in 16 h. What is the capacity of the tank? (a) 2346 L (b) 1600 L (c) 800 L (d) 960 L (e) None of the above 15. Two taps A and B can fill a tank in 25 min and 20 min, respectively. But taps are not opened properly, so the taps
(a) 12 min (b) 13 min (c) 14 min (d) 15 min (e) 16 min 16. Two taps A and B can fill a tank in 20 min and 30 min, respectively. An outlet pipe C can empty the full tank in 15 min. A, B and C are opened alternatively, each for 1 min. How long will the tank take to be filled? (a) 105 min (b) 120 min (c) 167 min (d) 185 min (e) 198 min Answer with Solutions Exercise© Base Level Questions
Exercise © Higher Skill Level Questions