Pipes and Cisterns PDF

Pipes and Cistern Pipe and cistern’ is the subtopic of ‘Time and work,’ so we need to remember all the concepts of ‘Time and work’ to excel in this topic. Cistern: Cistern is a tank for storing liquids generally water and has inlet and outlet pipes to fill or empty itself. Pipe: Pipe is a section...

Pipes and Cistern Pipe and cistern’ is the subtopic of ‘Time and work,’ so we need to remember all the concepts of ‘Time and work’ to excel in this topic. Cistern: Cistern is a tank for storing liquids generally water and has inlet and outlet pipes to fill or empty itself. Pipe: Pipe is a section of a hollow cylinder for the discharge of water from one place to another. Pipes are generally connected to the cistern/tank for filling and emptying the cistern or tank. Pipes are of two kinds: Inlet Pipe: Pipe, which fills a cistern or tank, is an inlet pipe. Outlet Pipe: Pipe, which empties a cistern or tank, is an outlet pipe. Pipes working together: Example: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively. If both the pipes are opened together, how long will it take to fill the cistern? Solution: A=20 B=30 Total work=60 units Working together they can complete 5 units of work in 1 day, and 60 units of work Will be completed in 12 days. Example: Three pipes A,B and C can fill a tank in 20 minutes, 30 minutes and 40 minutes respectively while working alone. If, all the pipes are opened together, how long will it take to fill the tank full? a)9.23 mins b)12.23 mins c)8.23 mins d)None of these Working on alternate minutes Example: A tap can fill a tank in 30 minutes. B can fill it in 45 minutes. If both the taps are opened on alternate min, in how much time the tank will be full?  1st min=3units Solution: A=30 2nd min=2units B=45 In 2 mins=5units In 36mins= 90 units Assumed capacity of the tank=90units A will fill 3units of water in the tank and on the next min. B will pour 2 units of water in the tank. In 2 mins 5 units of water will be poured in the tank, to fill 90 units of water in the tank, 36 mins are required. Example: Three tapes A, B, C can fill an overhead tank in 4, 6 and 12 mins respectively. How long would the three taps take to fill the tank if it is opened on alternate minutes? a)3mins b)5mins c)7.5mins d)None of these Inlet and outlet pipes working together Example: A can fill an empty tank in 15 hours and B can empty the tank in 20 hours. If all the pipes opened simultaneously, then how many hours required fill the full tank? Solution: A=15 B=20 A can fill 4units of water in the tank in 1 minute and in the same time B will take out 3 units of water from the tank and left with the 1 unit of water. It will take 60 mins to fill 60 units of water in the tank. Example: Two pipes can fill a cistern in 20 minutes and 30 minutes respectively. Third pipe can empty the tank in 40 minutes. If all the three pipes are opened together, how long it will take to fill the tank full? a)17.14mins b)18.14mins c)17.56mins d)None of these  Inlet and Outlet Pipes working on alternate minute: Example: A pipe can fill a tank in 3 min. B can empty it in 4 min. In how much time the tank will be full if the pipes are working on alternate mins? Solution: A=3 1st min=4units B=4 2nd min=3units removed in 2 mins = 1 unit of water in 16mins = 8 units of water in 17th min = 4 units of water A will pour 4 units of water in 1 min and B will take out 3 units of water in the next minute. In 2 mins only 1 unit of water will be left in the tank. Similarly in 16 mins 8 units of water will be poured in the tank and on 17th min, A will pour 4 units of water in the tank and the tank will be full. Example: There are two pipes a and b. A and b can fill and empty in 20 minutes and 30 minutes respectively. If both are open for 1 minute alternate, then how much time will an empty tank be full? a)120 min b)117 min c)115 min d)114 min Finding the actual capacity of the tank Example: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres per minute. When the tank is full, the inlet is opened and due to leak, the tank is empty in 8 hours. Find the capacity of the tank Finding the actual capacity of the tank Example: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres per minute. When the tank is full, the inlet is opened and due to leak, the tank is empty in 8 hours. Find the capacity of the tank Solution: A(outlet)=6 B(inlet+otlet)=8 Inlet pipe can fill the tank in 24hrs. In 1 minute, it can pour 4liters of water in the tank and took 24hrs to fill the tank. So the capacity of the tank is 1min=4litre 60min=4*60 24hrs=4*60*24=5760 liters Example: A leak in the bottom of a container can empty the full tank in 4 hours. An inlet pipe fills water at the rate of 3 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 6 hours. How many litres does the container hold? a)3600 b)2880 c)2160 d)1440 Practice Questions 1. Pipe A can fill a tank in 36 minutes and pipe B can fill it in 45 minutes. If both the pipes are opened to fill an empty tank, in how many minutes will it be full? a)15 b)18 c)20 d)25 2. Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled? a)7hrs 30min b)7hrs 45min c)8hrs 45min d)9hrs 30min 3. A tap can fill a tank in 25 minutes and another can empty it in 50 minutes. Find whether the tank will be filled up or emptied and in how many minutes if both working together? a)Tank is filled up in 50 minutes b)Tank is emptied in 25 minutes c)Tank is filled up in 25 minutes d)None of these 4. Two pipes A & B can separately fill a cistern in 220 minutes and 330 minutes. Together, they can fill the cistern in a)1 hour 32 minutes b)1 hour c)2 hour 12 minutes d)2 hours 5. A pipe can fill a tank in 12 hours and another can empty it in 24 hours. If both the pipes are used, with the first pipe running for 2 hours and second pipe running for 1 hour alternatively, how long will it take to fill the tank? (Consider starting with the first pipe) a)22 hrs 30 min b)21 hrs c)22 hrs d)23 hrs 6. Two pipes A and B can separately fill a tank in 12 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? a)9 min b)10 min c)11 min d)12 min 7. 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)480 liters b)600 liters c)720 liters d)800 liters 8. A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty, it? a)7 hours b)8 hours c)14 hours d)28 hours 9. 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)16 hrs b)20 hrs c)40 hrs d)25 hrs 10. Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom of the tank it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed? a)3a/2 hrs b)2a/3 hrs c)4a/3 hrs d)3a/4 hrs 11. Two taps can fill a tank in 12 min and 18 min respectively. Both the taps are kept open for 2 min and then the tap that fills the tank in 12 min is turned off. In how many more minutes will the tank be filled? a)9 b)12 c)13 d)10 12. 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? a)45 mins b)90 mins c)115 mins d)None of these 13. Tap A can fill a tank in 30 minutes and tap B can fill the same tank in 60 minutes. If both the taps are opened together for 5 minutes, and after that tap A stopped working, then in how much time remaining part of the tank can be filled? a)20mins b) 25 mins c) 30mins d) 45mins 14. A tank is fitted with two taps A and B. A can fill the tank completely in 45 minutes and B can empty the full tank in 1 hour. If both the taps are opened alternatively for 1 minute, then in how much time the empty tank will be filled completely ? a)117mins b)120mins c)119mins d)None of these 15. 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 16. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. Both the pipes are opened together but after 5 minutes pipe B is closed. What is the total time required to fill the tank a) 16.1/3 min b) 16.2/3 min c) 17.2/3 min d) 18.2/3 min e) None of these 17. 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 18. Three pipes P, Q and R can fill a tank in 12, 15 and 20 minutes respectively. If pipe P is opened all the time and pipe Q and R are opened for one hour alternatively. The tank will be full in a) 5hr b) 6hr c) 7hr d) 8hr e) None of these 19. 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 20 A pipe can empty a tank in 60 minutes alone. Another pipe whose diameter is twice the diameter of first pipe is also opened. Now find the time in which both pipe will empty the tank together. a) 8 min b) 10 min c) 12 min d) 14 min e) None of these