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Pipes and Cistern

by Placement Factory
Type: NoteCourse: Placement Preparation Specialization: Quantitative AptitudeOffline Downloads: 3Views: 76Uploaded: 1 month agoAdd to Favourite

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Placement Factory
Placement Factory
Pipe and cistern concept Pipes and cisterns are almost the same as time and work problems. There are two kinds of pipes. 1 Inlet pipe- it fills the tank. If a pipe fills a tank in x hours. 1 th x Then in 1 hours, it will fill part of the tank. 2 outlet pipe- it impties the tank. If a pipe impties a tank in y hours, then in 1 1 th y hour, it will empty part of the tank. We use the same LCM method to solve the questions as we use in time an work problems. But one thing should be kept in mind that the work of an outlet pipe is negative. Let’s understand a few problems. Q.1 Pipe A can fill a tank in 10 minutes and Pipe B can fill it in 5 minutes. Another Pipe can empty it in 15 minutes. If they are opened simultaneously then how much time will be required to fill the tank? SolutionA  10 B5 C  15 L.C.M= 30 In 1 min. A fills 30 30  3l , B fills  6l 10 5 and C empties l 30  2l 15 Tank filled in 1 hr= 3+6-2=7 So total time to fill the tank= min Q.2 Two pipes can fill a cistern in 1 hour and 75 minutes respectively. there is also an outlet C. if all the three pipes are opened together. The tank is full in 50 minutes. How much time will be taken by C to empty the full tank? Solution- Pipes and cisterns Page 1
A  60 B  75 L.C.M.  300 In 1 min, A fills 300  5l 60 B fills 300  4l 75 Hence in 50 min, A and B can fill Capacity of tank- 300 tank filled in 1 min= 5+4=9 l  9  50  450l l l 150 of tank was emptied by pipe c in 50 minutes. Hence in 1 minutes, Pipe C will empty So to empty full tank of 300 150  3l 50 l 300 3 It will take = 100 minutes Q.3 Two, taps A and B can fill a tank in 10 hours and 8 hours respectively . If both the taps are opened simultaneously them how many hours before tap B should be closed so that the tank fills in 5 hours.? SolutionA  10 B8 L.C.M  40 Hence in 1 hour, A will fill A remains open fill end. So A fills  5  4  20l 40  4l 10 and B will fill 40  5l 8 of the tank. ( in 5 hours) l Hence remaining 20 must be filled by B. l 20  4hours 5 So to fill 20 , B takes Q.4 Pipe A and B fill a cistern in 9 hours and 18 hours respectively but a third pipe C can empty the tank in 27 hours. If all the pipes are opened Pipes and cisterns Page 2
simultaneously but after 4 hours pipe C is closed, then calculate the time in which the tank will be filled? SolutionA9 B  18 C  27 L.C.M  54 l l l In 1 hour, A fill 6 , B fill 3 and C empties 2 . C is open only for 4 hours. Tank filled in 4 house = (6  3  2)  4  28l Tank to be filled after 4 hours =54-28=26 l 26 26  hours 63 9 l 26 will be filled by A and B in 5 Pipe A and B can fill a cistern in 12 minutes and 15 minutes respectively but a third pipe C can empty it in 6 minutes. The first two pipes are kept open for 5 minutes and then pipe C is also opened. Find the time taken to empty the cistern. SolA  12 B  15 C  6 L.C.M  60 l l l In 1 hour, A fills 5 , B fills 4 and empties 10 , A and b are open for initial 5 l minutes, which fill (5+4) =45 of tank. Now C is also open. So in 1 minute = 5+4-10=-1 L of tank is emptied. l So empty 45 , it will take 45 minutes. Pipes and cisterns Page 3
2 th 5 Q.6 A cistern is filled. A pipe A can fill it in 10 minutes and Pipe b can empty it in 6 minutes. If both pipes are opened simultaneously. How long will they take to empty the cistern. SolA  10 B  6 L.C.M  30 l l In 1 minute, A fills 3 . and B empties 5 of tank. But tank is 2 5 filled 2   30  12l 5 When both A and B are opened= 3-5=2 l l 2 of tank is emptied in 1 minutes. 12  2 l 12 of tank is emptied in 6 minutes 7. Pipe A and B can fill a cistern in 10 hours and 15 hours respectively. Both the pipes are open together to fill the tank, but when the tank is develop in the tank which empties by Pipe A and B to fill the cistern. Solution- 1 th 12 l l l Both are open so in 1 hour (3+2)=5 of tank is filled. Pipes and cisterns filled, a tank of water of the tank. Find the time taken A  10 B  15 L.C.M.  30 In 1 hour, A fills 3 and B fills 2  th 6 Page 4

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