Pipe and Cistern Exercise

Exercise 1. 2. 3. 4. Two pipes A and B can fill a tank in 20 minuuts and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is: (a) 50 min. (b) 12 min. (c) 25 min. (d) 15 min. Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened then the cistern is full in 50 minutes. In how much time the third pipe alone can empty the cistern? (a) 110 min. (b) 100 min. (c) 120 min. (d) 90 min. A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each, how soon will the cistern be filled? (a) 121 min. (b) 110 min. (c) 115 min. (d) 120 min. 6. 1 minutes and 45 2 minutes respectively. Both the pipes are opened. The cistern will be filled just in half an hour if the pipe B is turned off after: (a) 15 minutes (b) 10 minutes (c) 5 minutes 7. (a) 240 litres (b) 120 litres 80 litres 3 (d) 100 litres (c) 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) 4 hours Pipe and Cistern (d) 9 minutes A tank can be filled with water by two pipes A and B together in 36 minutes. If the pipe B was stopped after 30 minutes the tank is filled in 40 minutes. The pipe B can alone fill the tank in (a) 45 minutes (b) 60 minutes (c) 75 minutes (d) 90 minutes 8. 1 rd of tank holds 80 litres of 3 water, then the quantity of water 1 tank holds is : 2 Two pipes A and B can fill a cistern in 37 Two taps A and B can fill a tank in 48 min. and 36 min. If both the taps are opened together. After how much time tap A is closed so that the whole tank will be filled in 25 min. 30 sec. (a) 14 min If that 5. (b) 4 hours 15 minutes (c) 3 hours 15 minutes (d) 3 hours 45 minutes (b) 18 min 9. 1 rd of the water supply by both 3 the pipes leaks out. Then calculate in how much time the tank will be full ? (a) 16 hours (b) 12 hours (c) 18 hours (d) None of these 10. If taps A and B can fill a tank in 15 hours and 20 hours respectively. Both the taps are opened together when the tank is 1 th 4 full, a leak develops in the bottom of the tank . Through which 1 th of water supply by both the 5 pipes leaks out. Then calculate in how many hours the tank will be full ? (a) 10 (c) 1 5 5 days (b) 11 days 28 28 5 days 28 (d) None of these 11. In a tank four taps of equal efficiency are fitted on equal intervals. The first pipe is at the base of the tank. And the 4th pipe 3 th of height of the tank. 4 (c) 14 min 30 sec is at (d) 15 min 30 sec Then calculate in how much time the whole tank will empty. If the first pipe can empty the tank in 12 hours. Taps A and B can fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill 1 the tank but when the tank is rd 3 full, a leak develops in the bottom of the tank, through which (a) 6 hours 15 min. (b) 7 hours 15 min. (c) 8 hours 20 min. (d) None of these 12. Two taps A and B can fill a tank in 30 min and 36 min respectively. Both taps are opened together but due to some 5 9 problem they work and of 6 10 their efficiencies, after some time the problem was removed and 1 min. 2 Then after how much time the problem was removed. (a) 1 minutes (b) 2 minutes now the tank will fill in 16 (c) 3 minutes (d) 1 1 minutes 2 13. Two taps A and B can fill a tank in 10 hours and 12 hours respectively. There is an outlet tap C. If all the taps are opened together the tank will fill in 30 hours. In how many hours tap C can alone empty the tank. (a) 60 hours 7 (b) 60 hours 9 (c) 60 hours 11 (d) 60 hours 13 14. A leak in the bottom of a tank can empty it in 6 hours. A tap fills the tank at the rate of 4 litres/ min is turn on. If both the taps are opened then the tank will empty in 8 hours. Find the capacity of the tank? (a) 2400 litres (b) 5780 litres (c) 5760 litres (d) None of these 15. A leak in the bottom of a tank can empty it in 12 hours. A tap which can fill 20 litres of water per minute is turned on. Both the taps are opened now, then the tank is emptied in 20 hours. Find the capacity of the tank ? (a) 36000 litres (b) 3600 litres (c) 360 litres (d) None of these 16. 8 taps are fitted in a tank some are inlet taps and rests are outlet tap. Each inlet tap can fill the tank in 12 hours and each outlet tap can empty it in 36 hours. Then calculate the number of inlet water taps if the whole tank filled in 3 hours. (a) 5 (b) 3 (c) 4 (d) None of these 17. 9 taps are fitted in a tank some are inlet taps and some are outlet taps. Each inlet tap can fill the tank in 9 hours and each outlet tap can empty the tank in 9 hours. If all the taps are open then tank will be full in 9 hours, then find the number of outlet taps. (a) 4 (b) 5 (c) 3 (d) None of these 18. 12 taps are fitted in a tank some are inlet taps and some are outlet taps. Each inlet tap can fill the tank in 6 hours and each outlet tap can empty the tank in 12 hours. If all the taps are open together then the tank will be full in 4 hours. Then find the number of inlet taps. (a) 5 (b) 4 (c) 6 (d) None of these 19. Tap A and B can fill a tank in 10 hours and 20 hours respectively. Tap C can empty it in 12 hours. If all the taps are open alternatively for 1 hour each then the whole tank will be filled in how many hours. ? (a) 40 (b) 20 2 hours 3 1 hours 3 2 hours 3 (d) None of these 20. Pipe A can fill a tank in 12 hours and pipe B can fill it in 15 hours, separately. A third pipe C can empty it in 20 hours. Initially pipe A was opened, after one hour pipe B was opened and then after 1 hour when pipe B was opened pipe C was also opened. In how many hours the tank will be full? (c) 8 (a) 9 2 2 hours (b) 6 hours 3 3 (c) 10 hours (d) None of these 21. A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is plugged. If both pipes are opened simultaneously at a time when the tank was one-third filled, when will be the tank full thereafter? (a) 3 hours 2 (c) 2 hours (b) 2 hours 3 (d) 1 2 hours 3 22. An inlet pipe can fill a tank in 5 hours and an outlet pipe can empty the same tank in 36 hours, working individually. How many additional number of outlet pipes of the same capacity are required to be opened, so that the tank never overflows ? (a) 3 (b) 6 (c) 8 (d) 7 23. In a public bathroom there are n taps 1, 2, 3...n. Tap 1 and Tap 2 take equal time to fill the tank while tap 3 takes half the time taken by tap 2 and tap 4 takes half the time taken by tap 3. Similarly each next number of tap takes half the time taken by previous number of tap i.e., Kth tap takes half the time taken by (K – 1)th tap. If the 8th tap takes 80 hours to fill the tank the 10th and the 12th tap working together take how many hours to fill the tank? (a) 2 hours (b) 4 hours (c) 6 hours (d) None of these 24. Pipe A takes 3/4 of the time required by pipe B to fill the empty tank individually. When an outlet pipe C is also opened simultaneously with pipe A and pipe B, it takes 3/4 more time to fill the empty tank than it takes normally when only pipe A and pipe B are opened together. If it takes 33 hours to fill when all the three pipes are opened simultaneously, then in what time pipe C can empty the full tank operating alone ? (a) 66 hours Pipe and Cistern (b) 50 hours (c) 44 hours (d) can't be determined 25. A tank is connected with 8 pipes. Some of them are inlet pipes and rest work as outlet pipes. Each of the inlet pipe can fill the tank in 8 hours, individually, while each of those that empty the tank i.e., outlet pipe, can empty it in 6 hours individually. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are inlet pipes? (a) 2 (b) 4 (c) 5 (d) 6 26. A tank has two inlet pipes which can fill the empty tank in 12 hours and 15 hours working alone and one outlet pipe which can empty the full tank in 8 hours working alone. The inlet pipes are kept open for all the time but the outlet pipe was opened after 2 hours for one hour and then again closed for 2 hours then once again opened for one hour. This pattern of outlet pipe continued till the tank got completely filled. In how many hours the tank has been filled, working on the given pattern? (a) 8 hours 24 min. (b) 10 hours 15 min. (c) 9 hours 10 min. (d) 9 hours 6 min. 27. A, B, C are three pipes attached to a cistern. A and B can fill it in 20 and 30 minutes respectively, while C can empty it in 15 minutes. If A, B, C are kept open successively for 1 minute each, how soon will the cistern be filled? (a) 167 min. (b) 160 min. (c) 166 min. (d) 164 min. 28. A bath can be filled by the cold water pipe in 10 minutes and by the hot water pipe in 15 minutes. A person leaves the bathroom after turning on both the pipes simultaneously and returns at the moment when the bath will be Pipe and Cistern full. Finding however, that the waste pipe has been open, he now closed it. In 4 minutes more the bath is full. In what time would the waste pipe empty it. (a) 9 min. (b) 8 min. (c) 12 min. (d) 6 min. 29. Pipe A takes 4 minutes more to fill the cistern than two pipes A and B opened together to fill it. Second pipe B takes 9 minutes more to fill cistern than two fill pipes A and B opened together to fill it. When will the cistern be full if both pipes are opened simultaneously. (a) 4 minutes (b) 6 minutes (c) 5 minutes (d) 7 minutes 30. Two pipes can fill a cistern in 30 and 15 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 5 hours extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it? (a) 60 hours (b) 45 hours (c) 35 hours (d) 30 hours 31. There are 12 filling pipes each capable of filling a cistern alone in 32 minutes and 8 emptying pipes each capable of emptying A cistern alone in 40 minutes. All pipes are opened together and as a result, tank was filled with 28 litres of water per minute. Find the capacity of the tank. (a) 160 litres (b) 120 litres (c) 100 litres (d) 80 litres 32. Three pipes A, B and C are connected to a tank. A and B together can fill a tank in 60 minutes, B and C together in 40 minutes and C and A together in 30 minutes. In how much time will each pipe fill the tank separately? 33. If two pipes function simultaneously, the reservoir is filled in 6 hours. One pipe fills the reservoir 5 hours faster than the other. How many hours does the faster pipe takes to fill the reservoir ? (a) 20 hours (b) 10 hours (c) 15 hours (d) 12 hours 34. One filling pipe A is 5 times faster than second filling pipe B. If B can fill a cistern in 36 minutes, then find the time when the cistern will be full if both the fill pipes are opened together. (a) 6 minutes (b) 8 minutes (c) 4 minutes (d) 12 minutes 35. In what time would a cistern be filled by three pipes whose diameters are 1 cm, 2 cm, 4 cm, running together. When the largest 1 hours, the 20 amount of water flowing in by each pipe being proportional to the square of its diameter. alone fill it in 1 (a) 38 minutes (b) 42 minutes (c) 44 minutes (d) 48 minutes 36. Two pipes A and B can fill a cistern in 20 minutes and 25 minutes respectively. Both are opened together, but at the end of 5 minutes, B is turned off. How much time will the cistern takes to be filled? (a) 16 minutes (b) 18 minutes (c) 11 minutes (d) None of These 1 minutes 2 more to fill the cistern than two fill pipes A and B opened together to fill it. Second fill pipe B takes 8 minutes more to fill the cistern than two fill pipes A and B opened together to fill it. When will the cistern be full if both the pipes are opened simutaneously. 37. One fill pipe A takes 4 (a) 80 min, 240 min, 48 min (a) 8 min. (b) 6 min (b) 40 min, 120 min, 24 min (c) 11 min. (d) None of these (c) 60 min, 250 min, 64 min (d) 65 min, 240 min, 64 min 38. Two fill pipes A and B can fill a cistern in 18 and 24 minutes respectively. Both fill pipes are opened together , but 6 minutes before the cistern is full, one pipe A is closed. How much time will the cistern takes to be full. (a) 12 4 min. 7 (b) 12 5 min 7 (c) 13 5 min. 7 (d) None of these 39. A cistern can be filled by two pipes filling separately in 12 and 16 minutes respectively. Both pipes are opened together for a certain time but being clogged, only 7/8 of full quantity water flows through the former and 5 only through the latter pipe. 6 The obstructions, however being suddenly removed, the cistern is filled in 3 minutes from that moment. How long was it before the overflow began? 1 1 (a) 4 min. (b) 4 min. 3 2 1 1 (c) 3 min. (d) 8 min. 2 3 40. A cistern can be filled by one of the two pipes in 30 minutes and by the other in 36 minutes. Both pipes are opened together for a certain time but being 5 particularly Clogged, only of 6 the full quantity of water flows 9 through the former and only 10 through the latter. The obstructions, however, being suddenly removed, the cistern is 1 minutes from that 2 moment. How long was it before the overflow of water began? (a) 1 min. (b) 2 min. filled in 15 1 min. 2 41. Three pipes A, B, and C are attached to a cistern. A can fill it in 10 minutes and B in 15 minutes. C is a waste pipe for emptying it. After opening both the pipes A and B, a man leaves the cistern and returns when the (c) 5 min. (d) 1 cistern should have been just full. Finding however, that the waste pipe has been left open, he closes it and the cistern is now full in 2 minutes. In how much time the pipe C, if opened alone, empty the full cistern. (a) 18 min. (b) 16 min. (c) 12 min. (d) None of these 42. Three pipes A, B, and C are attached to a cistern. A can fill it in 20 minutes and B in 30 minutes. C is a waste pipe meant for emptying it. After opening both the pipes A and B, a man leaves the cistern and returns when the cistern should have been just full. Finding however, that the waste pipe has been left open, he closes it and the cistern now filled in 3 minutes. In how much time the pipe C, if opened alone, empty the full cistern? (a) 18 min. (b) 16 min. (c) 12 min. (d) None of these 43. Pipe A can fill a tank in 12 hours. Due to development of a hole in 1 the bottom of the tank rd of the 3 water filled by the pipe A leaks out. Find the time when the tank will be full. (a) 18 hours (b) 12 hours (c) 36 hours (d) None of these 44. Two pipes A and B can fill up a half full tank in 1.2 hours. The tank was initially empty. Pipe B was kept open for half the time required by pipe A to fill the tank by itself. Then, pipe A was kept open for as much time as was 1 required by pipe B to fill up of 3 the tank by itself. It was found 5 that the tank was full. The 6 least time in which any of the pipes can fill the tank fully is : (a) 4.8 hours (b) 4 hours (c) 3.6 hours (d) 8 hours 45. A tank of capacity 25 litres has an inlet and an outlet tap. If both are opened simultaneously, the tank is filled in 5 minutes. But if the outlet flow rate is doubled and taps are opened then the tank never gets filled up. Which of the following can be outlet flow rate in litres/min? (a) 2 (b) 6 (c) 4 (d) 3 46. Two taps are running continuously to fill a tank. The Ist tap could have filled it in 5 hours by itself and the second one by itself could have filled it in 20 hours. But the operator failed to realise that there was a leak in the tank from the beginning which caused a delay of one hour in the filling of the tank. Find the time in which the leak would empty the filled tank. (a) 15 hours (b) 20 hours (c) 25 hours (d) 40 hours 47. A cistern can be filled by two pipes filling separately in 36 min and 48 min respectively. Both pipes are opened together for a certain time but being jammed, 4 only of full quantity water 5 flows through the former and 3 through the latter pipe. 5 The obstruction, however being suddenly removed, the cistern is filled in 17 minutes from that moment. How long was it before the overflow began? (a) 6 min (b) 5 min (c) 4 min (d) None of these 48. A cistern can be filled by two pipes filling separately in 30 min and 36 min respectively. Both pipes are opened together for a certain time but being jammed, 5 only of full quantity water 6 flows through the former and 9 only through the latter pipe. 10 The obstruction, however being suddenly removed, the cistern is 1 filled in 15 minutes from that 2 moment. How long was it before only Pipe and Cistern the overflow began? (a) 1 min. (b) 2 min. 1 1 min. (d) 2 min. 2 2 49. Four pipes A, B, C and D are attached to a cistern. A can fill it in 20 min. B in 30 min and C in 60 minutes. D is a waste pipe for emptying it. After opening all the three pipes A, B and C a man leaves the cistern and returns when the cistern should have been just full. Finding however, empty in 80 hours. If the pipe A is opened at 7 am and the pipe B at 9 am and the third pipe C at 12:00 noon. Then after how much time the tank will be filled? that the waste pipe has been left open, he closes it and the cistern now gets filled in 3 minutes. In how much time the pipe D, if opened alone, empty full cistern. (c) 1 (a) 33 1 1 min (b) 32 min. 3 3 2 2 min. (d) 33 min. 3 3 50. Two pipes A and B can fill a cistern in 40 and 50 hours respectively, and a third pipe C can (c) 32 (a) 1 1 pm on next day 13 (b) 2 1 pm on next day 13 (c) 2 1 pm on next day 11 (d) None of these Solution 1. (b) A 20 min 3 60 (capacity of Tank) B 30min 2 A & B together to fill the tank in = 2. 5. 60 = 12 minutes 5 300 (capacity of tank) B  30 min \ Q \ +3 60(Capacity of Tank) –2 Tank filled by A in 1 min. = 1 × 3 = 3 units Tank empty by B in 1 min. = 1 × 2 = 2 units Tank filled in 2 min. = 3 – 2 = 1 unit 1 unit tank fill in 2 min. 60 units tank fill in 2 × 60 = 120 min. 1 rd tank = 80 lit. 3 4. (b) Q \ full tank = 80 ×3 = 240 lit. Hence, the quantity of water that holds half of the tanks Pipe and Cistern D 3 = 3hrs. 1 Time tanken by all the pipes to 3 fill the remaining half tank = 4 3 hrs = × 60 = 45 min 4 Total time taken to fill the tank tank = 300 = 100 minutes 3 (d) A  20 min C Q Time taken by A to fill the half Eff. of IIIrd pipe = 5 + 4 – 6 = 3 units III rd Pipe alone empty the tank 3. B \ Hence, B is turned off after 9 min. (d) Tank filled by B in 30 min = 1 1 1 1 A A  60 min 5 B  75 min 4 A+B+IIIrd  50 min 6 7. \ (b) = 240 = 120 lit. 2 (d) Let the pipes are A,B,C & D having same efficiencies. 6(capacity of tank) = 30 5 = 36 6 Remaining part of tank = 1– 1 th tank is completed in (40–30) 6 = 10 min (d) 37 Time taken by \ Time taken by A to fill the full tank = 6 × 10 = 60 min. 180 3 A 1 75 min. = min 2 2 225 units 6 A 75 min 45 min. 2 A fills the tank in 30 min = 30 × 6 = 180 units Remaining = 225 –180 = 45 units Time taken by B to fill the tank 45 45 units = = 9 min 5 5 B 60 min A+B 36 min \ efficiency of B = 5 – 3 = 2 units Time taken by B to fill the tank 8. 180 = 90 min 2 (a) A 48 3 units/min 5 B 1 th tank = 10 min 6 \ = 3 hrs 45 min 6. 5 1 = 6 6 = B 36 144 4 units/min Total capacity of the tank According to the question, Tap B would be open till the end so part filled by pipe B in 25 min 30 sec. = 4× 51 = 102 units 2 é êë \ ù 51 min ú û 2 25 min 30 sec = Reamining capacity of the tank = (144 – 102) = 42 units This remaining part is filled by pipe A. 42 = 14 min 3 So pipe A should be closed after 14 min. So required time = 9. (a) A B 20 I st Pipe 3 units Now leaks has been developed. leaked out water 1 5 = units/hour 3 3 Now required time to fill the rest capacity of the tank = 5 40 40  3  12 hours = = 10 5  5 –   3  Total time to fill the tank = 12 + 4  16 hrs 10. (a) A 15 4 B 20 3 60 Total capacity of the tank According to the question, Time required for filling of the tank 1 th part 4 Now leaks have been develop.  Leaked out water 1 7 = units/hour 5 5 Now required time to fill the rest capacity of the tank = 7 45 45  5 = 7 = 28 7– 5 Total time = rd III Pipe II 3 units 225 = 28 225 15 + 28 7 30 If both pipes A and B working with original efficiency then filled 1 part in 16 min 2 60 hours 9 A ( leak) 6 hours –4 A+B 8 hours –3 B (filling pipe) are opened together so they leaks out 3 units/hour.  Efficiency of filling pipe = (4 – 3) = 1 unit/hour Required time for B (filling pipe) to fill the tank = Extra units = 363 – 360 = 3 units Now efficiency after problem occured:- 5  12 6 = 10 units/min 9 10 = 9 units/min Combined efficiency = (10 + 9) = 19 Difference between original and new efficiency 24 Capacity of the tank 4 units/hour and now both A (Leak) and 33 = × (10+12) = 33 × 11 = 363 units 2 Efficiency of B = 10  60 Total capacity of the tank It means in starting Leak A leaks out 30 12units/min 360 Total capacity 36 10 units/min Efficiency of A = 5 2 According to the question:- 3 1 = 6 = 6 hours 15 min 12 4 B A+B+C 6 14. (c) Let A be the leakage and B be the filling pipe. 9  12  18  36 75 = = 12 12 12. (a) A 12 tank = 3 3 3 3 + + + 2 4 3 1 = 6 B Required time for C to empty the I Pipe Time required to empty the tank 10 Efficiency of tap C = [( 6 + 5 )–2] Pipe According to the question:All the pipes are set on equal intervals. A = 9 units/hour st This is because we did not count the problem time. 60 15 = = hours 4´ 7 7 13. (b) According to the question:- IV Pipe nd 3 = 1 min 3 So we can say after 1 min the problem was removed. Total capacity of tank 3 units = = th 3 units 60 Total capacity 30 2 units/hr of the tank Now Required time to fill 3 units –1 3 th 3 height =  12 = 9 4 4 According to the question :-  12 12 3 units/hr 1 Required time for filling rd of the 3 60  1 tank = 3 3  2 = 4 hours   = (22 – 19) = 3 units/min 285 5 = 10 hours 28 28 11. (a) Let the capacity of the tank be 12 units = 24 = 24 hours 1 And pipe B fills 4 litres/min [Given]  Capacity = 4 × 24 × 60 = 5760 litres 15. (a) Let A be the leakage and B be the filling pipe. According to the question:A ( leak) 12 hours –5 A+B 20 hours –3 60 Total Capacity of the tank It means in starting leak A leaks out 5 units/hour and now both filling pipe (B) and leak (A) are opened together Pipe and Cistern so they leak out 3 units/hour.   Efficiency of filling pipe = (5 – 3) = 2 units/hour x –9x 1 = 9 9 2x – 9 = 1  60 = 30 hours 2 And pipe B fills 20 litres/min [ Given ]  Capacity of the tank = 20 × 30 × 60 = 36000 litres 16. (a) inlet tap Outlet tap 12 3 –36 –1 36 Total Capacity of the tank According to the question :Required time to fill the tank = 3 hours   : : 20 5 : : Outlet taps –8     Number of inlet water taps = 5 and, Number of outlet taps = (12 – 5) = 7 10 B 20 = 1 3x – 8  x = 3 36 C the number of outlet taps = (9 – x) According to the question:- Pipe and Cistern Water filled by the pipe A in 2 hours = 5 × 2 = 10 units Water filled by the pipe B in 1 hour = 4 × 1 = 4 units Total water filled – 6 3  60 – 14 46  5  4 – 3 = 6 = 23 3 = 23 2 = 9 hours 3 3 21. (c) Let A be the inlet pipe and B be the outlet pipe. A 2 60 Total capacity of tank –12 –5 = ( 6 + 3 – 5) = 4 units Time : Work done 3 hours 4 units   × 13 39 hours 52 units Remaining work = (60 – 52) = 8 units Work done by A on 14th hr = 6 units 3 6 Total Capacity of the tank –6 –1 –B Water filled by all the three pipes (A + B + C) in 3 hours  × 13  Total time = 12 + x = 5 A 17. (a) Let the number of water taps = x –20 60 Total capacity of tank Now all the pipes will work together. Required time x 8–x – 12 36 Number of inlet pipes = 5 and, Number of outlet pipes = (8 – 5) = 3 – 5 4 –3 12 – x  x 1 – =  6 12 4 =  x = 5 15 = (10 + 4) = 14 units For alligation method refer question no. 16. 19. (a)  4x = 20 B According to the question:- the outlet pipes = (8 – x) According to the question :-  4x – 8 = 12 12 2 2 = 40 hr 3 3 According to the question:- the number of outlet taps = (12 – x) Alternatively: 1 3 A C Let the number of filling pipes = x =  Number of water taps = 5 and, Number of outlet taps = (9 – 5) = 4  3x = 15 Required number of water taps Alternatively:- 20. (a) 2x – 12  x 1 =  12 4  3x – 12 = 3 12 3 8 5 = 5 = (5  3) x =5 18. (a) Let the number of water taps = x 12 Ratio of tapes = 39 + 1 + For alligation method refer question no. 16. 36 Avg. efficiency = = 12 units/hrs 3 Now By alligation method :inlet taps 24 Total Required time Alternatively:  2 hr 3 Required time =  Required time for B (filling pipe) to fill the tank = 9 – x  1 x – = 9 9 9 Remaining part of the tank 2 = 4 units 3 Required time to fill the tank 4 = 3 – 1 = 2 hours   = 6× 22. (c) Let A be the inlet pipe and B be the outlet pipe. A B 5 +36 –36 –5 180 Total Capacity of the tank æ36 ö = 7.2 ÷ ÷ è 5 ø Since, an inlet pipe çç times efficient than an outlet pipe. Therefore inorder to tank never overflow we will need total 8 outlet pipes. 23. (b) 8th tap : Remaining work = (8 – 6) =2 units Time :- 9th tap : 10th tap : 20 hrs. 80 hrs. 40 hrs. ×½ ×½ ×½ th 11th tap : 12 tap 10 hrs. ×½ 5 hrs. 10th tap 20 12th tap 5 1 20 Total Capacity (units) 4 20 = (8 – 4) = 4 26. (c) Let A and B are the inlet pipes and C is the outlet pipe. Required time = 4 +1 ( ) = 4 hours 24. (c) Let the time taken by pipe B = 4x  Time Taken by pipe A A B 3x 33 B 44 – A+B+C 33 4 3 4 132 Total capacity of the tank = 132 = 44 hours 7 – 4 25. (b) Let the number of inlet pipes =x The number of outlet pipes = (8 – x) According to the question:  8 – x  6 – x 1 = 8 6 = (10 + 8 – 15) = 3 units  Time Filled (Water) 3 hours 39 units  ×3  ×3 9 hours 117 units Now remaining capacity of the tank = 120 – 117 = 3 units Now only pipes A and B are open.  Required time = 3 10  8  1 ×60 = 10 minutes. 6 Total time = 9 + 10 minutes = = 9 hrs. 10 min. 27. (a) A 20 3 – C 30 –15 2 60 –4 Total capacity of tank ( units ) water filled by all the three pipes (A + B + C ) in 1 min = (3 + 2 – 4) = 1 unit Time : Filled Capacity 3 min  1 unit  × 55  × 55 165 min 55 units Remaining capacity 32 – 4x – 3x 1 = 24 6 –7x + 32 = 4  = (60 – 55) = 5 units  x = 4 Remaining part = (5 – 3) = 2 units Number of inlet pipes = 4 and, Number of outlet pipes 2 Required time by B = = 1 min. 2   –15 –8 B Time required by the pipe ( C ) 120 Total capacity of tank Water filled in the third hour 12 12x 3 x  = 33 7 7 4 12x  9x = = 33 7 A 8 Now for the next hour all the three pipes are open. = Now required time by pipe A = 3×11 = 33 hours and required time by pipe B = 4 × 11 = 44 hours 15 = (10+8)× 2 = 36 units According to the question: 21x = 33  x = 11 7 B Water filled by the pipes A and B in the first two hours 12x Total Capacity of the tank 4x 3 Required time by (A + B)  10 – 4 12x 12x = = 7  4  3 12 C 3 × 4x = 3x 4 = A In 166th min the pipe A will work so filled part = 3 units Total time = 165 + 1 + 1 = 167 min 28. (a) Let the cold water pipe be A and the hot water pipe be B. A 10 3 B 15 Total capacity of the tank 30 2 Required time by (A + B) to fill 30 the tank =  2  3  = 6 min According to the question:Water filled by the pipes (A + B) in 4 minutes = 4 × 5 = 20 units Now it is emptied by the waste pipe (C) in 6 min. Required time by the waste pipe (C) to empty the whole tank = 30 × 6 = 9 min 20 29. (b) Note: In such type of questions use this method to save your valuable time. Let the time taken by the pipes (A + B) = x min According to the question :A : A+B : B x+4 : x : x+9 Required time = 30. (d) A 30 B 15 1 30 2 4  9 = 6 min Total capacity of the tank Required time for (A + B) to fill 30 the cistern = = 10 hours 1  2 According to the question: When leakage is open then, required time = (10 + 5) = 15 hours A+B 10 A+B+C 15 3 30 2 Capacity [here C = Leak pipe ] Efficiency of the leak = ( 3 – 2 ) = 1 unit/hr Required time for leak to empty the tank = 30 = 30 hours 1 31. (a) Pipe and Cistern  x2 – 10x + 3x – 30 = 0 A 20  x (x – 10) +3 (x – 10) = 0 B 25 Efficiency of 12 filling pipes  (x – 10) (x + 3) = 0 = 12 × 5 = 60 litres/min x = 10 hours Efficiency of 8 emptying pipes Time taken by the faster pipe A = 10 hours Water filled by the pipes (A + B) in 5 minutes = 9 × 5 = 45 units Remaining capacity of the tank = (100 – 45) = 55 units Required time for A to fill the remaining part Filling pipe (A) 32 5 litres/min 160 Capacity (litres) –40 –4 litres/min Emptying pipe (B) = 8 × –4 = – 32 litres/min Net efficiency = (60 – 32) = 28 litres/min According to the question: Capacity of the tank = = 160 litres 32. 28  160 28 Note :- In such type of questions always take help from options to save your valuable time. As : Option (b) = 2 units/min Time taken by the faster pipe A B+C 40 3 = 10 hrs A Time taken by the slower pipe B = 15 hrs. B 4 30 120 Total capacity of tank =  2  3  4 2 = 4.5 units/min Efficiency of C = (4.5 – 2) = 2.5 units/min Efficiency of B = (4.5 – 4) = 0.5 unit/min Efficiency of A = (4.5 – 3) = 1.5 units/min Required time byA to fill the tank 120 = = 80 min 1.5 Required time by B to fill the tank 120 = = 240 min 0.5 Required time by C to fill the tank 120 = = 48 min 2.5 33. (b) Let the time taken by the faster pipe A = x hours Then the time taken by the slower pipe B = (x + 5) hours x x+5 (x+5) x x (x+5) Total capacity of the tank According to the question:- x  x  5 x   x  5 =6  x2 + 5x = 12x + 30  x2 – 7x – 30 = 0 Pipe and Cistern A 10 3 B 15 2 Required time for (A + B) to fill the 30 tank = 3  2 = 6 hours   34. (a) A : B Efficiency:- 5 : 1 Time :- : 5 [ 1 Efficiency  = 1 2 2 +  2 +  4  2 2 63  16   48 minutes 1 + 4 + 16 36. (a) 80 = 16 min 5 9 8 2 = 6 minutes 38. (c) A 18 B 24 4 72 3 Total capacity ( in units ) Let the cistern be filled in x minutes.  Pipe B is opened for x minutes and pipe A is opened for (x – 6) minutes. Now According to the question:3x + 4 (x – 6) = 72 3x + 4x – 24 = 72 7x = 96 1 35. (d) 1 hours = 63 minutes 20  4 100 Total capacity ( in units ) 25 4 According to the question :- 37. (b) Required time = 36 = 6 minutes 5   1 63  5 Required time = Required time for both the pipes According to the question :Required time 20 = (100 – 20) = 80 units = 36 units (A + B) = 55 = 11 minutes 5 Remaining capacity of the tank 1 ] Time Capacity of the tank = 36 × 1 Total capacity ( in units ) Water filled by the pipe B in 5 minutes = 4 × 5 = 20 units 30 Total capacity of the tank Now check the question conditon. So it is same Hence, option (b) is correct. 100 4 Total time for filling = (11 + 5) = 16 minutes Alternatively:- 60 Efficiency of (A + B + C) B Alternatively: (a) A+B C+A A Time taken by the slower pipe B = (10 + 5) = 15 hours 5 96 5 = 13 min. 7 7  x= Alternatively:A 18 B 24 4 72 3 Total capacity ( in units ) Water filled by the pipe A in 6 minutes = 6 × 4 = 24 units Total capacity = 24 + 72 = 96 units 96 96 Required time = 4  3 =   7 5 = 13 min 7 39. (b) A 12 min B 16 min 4 units/hr 48 3 units/hr Total capacity of the tank Let both pipes remain clogged for x minutes and hence full flow began after x minutes only.  Part of cistern filled in x min + part of cistern filled in 3 minutes = Cistern filled 30  6 = 18 min. 10 42. (d) A 20 min 3 units/min B 30 min 2 units/min 60 Total capacity ( in units ) Required time by (A + B) to fill the tank 60 = 3  2 = 12 minutes   7 5    4  x + 3× x  + 3  4  3 8 6   = 48 =  6x = 27 x = 4.5 min. 40. (a) A 30 min 6 units/min B 36 min 5 units/min 180 Total capacity (Let both the pipes clogged for x minutes) and hence full flow began after x minutes only. According to the question: 5 9  31  x+  6  x + 5× 6  5 6 10  2  = 180 5x + 9 31  11 x = 180 – 2 2 19 19 x = 2 2 x = 1 min  41. (a) A 10 min 3 units/min B 15 min 2 units/min 30 Total capacity ( in units ) Required time by (A + B) to fill the tank = 30 (3  2) = 6 minutes According to the question:Water filled by the pipes (A + B) in 2 minutes = Water emptied by the pipe C in 6 min  = According to the question:Water filled by the pipes (A + B) in 3 minutes = water emptied by the pipe C in 12 minutes Efficiency of the pipe C 6x + 21 = 48 Efficiency of the pipe C = 2   3  2 6 = 10 units/min 6 Required time for the pipe C to Required time for B to fill the tank 12 = = 6 hours 2 5 4 6 × 12 2 + 3 = 6 2 3 10 = 10 empty the tank 3(3  2) 5 = units/min 12 4 Required time for the pipe C to empty the tank = 60  4 = 48 min 5 43. (a) A 12 hours 1 unit/hr 12 Both sides are equal so option (b) is correct. 45. (b) Efficiency of inlet and outlet tap 25 = = 5 litres/min 5 The net inflow when both pipes are opened is 5 litres/min. The outlet flow should be such that if its rate is doubled the net inflow rate should be negative or zero. Only an option greater than or equal to '5' would satisfy this condtion. Option (b) is the only possible value. 46. (b) st I tap Total capacity ( in units ) II According to the question:Efficiency of the leakage = – unit/hr Combined efficiency of (A + Leak) 2 1 =1– = units/hr 3 3 Required time to fill the tank A +B 4 3 units/hr 12 5 5 units/hr 12 Total capacity ( in units ) Efficiency of B = (5 – 3) = 2 units/hr. Now satisfy question conditon:Required time for A to fill the tank = 4 hours 4 20 hours 1 Total capacity ( in units ) 20 = 4 hours According to the question :When leak is open then time taken = (4 + 1) = 5 hours I + II 4 5 I + II + Leak 5 4 20 Total capacity ( in units ) Efficiency of the leak = (5 – 4) = 1 unit/hr Required time for leak = 20 1 = 20 hours 47. (b) 12 A + B takes (2.4 = ) hours to 5 fill the tank. A tap 5 hours 20 Required time for (I +II) = 4  1   1 3 12  3 = = 18 hours 2 44. (b) Note : In such type of questions go through options to save your valuable time. Then satisfy the question conditions. Option (b): Let the pipe A takes least time = 4 hours According to the question:- nd  A 36 min 4 units/min B 48 min 3 units/min 144 Total capacity ( in units ) Let both the pipes remain jammed for x min hence full flow began after x minutes only. part of cistern filled in x min + part of cistern filled in 17 min = cistern filled 4 3    4  x + 3× x  +17 × 7 = 144 5 5   Pipe and Cistern A B 30 min 6 units/min 180 Total capacity 36 min 5 units/min ( in units ) A 20 min 3 units/min B 30 min 2 C 60 min = cistern filled 5 9   31 x + × 11  6  x + 5× 6 10 2   = 180 3   3  2  1 10 = 9 units/min 5 19 x = 180 – 341 2 2 Required time for pipe D to empty the tank 19 19 x =  x = 1 min 2 2 60  5 100 1 = = = 33 min 9 3 3 Pipe and Cistern B 8 C –80 hours 400 Total capacity ( in units ) –5 units/hr Remaining capacity of the tank = (400 – 74)units = 326 units Now all the three pipes (A + B + C ) simultaneously :- Efficiency of the pipe D = 10 units/hr 50 hours Total water filled = 50 + 24 = 74 units Water filled by the pipes (A + B + C) in 3 minutes = water emptied by the pipe D in 10 minutes.  40 hours Till 12:00 noon water filled by the pipe B = 8 × 3 = 24 units According to the question:- 31 min 2 A Till 12:00 noon water filled by the pipe A =10 ×5 = 50 units 60 = 3  2  1 = 10 minutes   part of cistern filled in x min + part of cistern filled in 60 Total capacity ( in units ) 1 unit/min Required time for (A + B + C) to fill the tank Let both pipes remain jammed for x min, and hence full flow began after x minutes only.  50. (a) 49. (a) 16x 9x + = 25 5 5 x = 5 min 48. (a)  will work Required time for (A + B + C ) 326 326 1 = 10  8 – 5 =   13 = 25 13 hrs It means the tank will be filled at 1 1 PM on the next day. 13