Pipe and Cistern Examples

11 PIPE AND CISTERN Examples 1. A tank is fitted with two taps. The first tap can fill tank competely in 45 minutes and the second tap can empty the full tank in one hour. If both the taps are opened alternately for one minute, then in how many hours the empty tank will be filled completely? Sol. (b) According to the question X Y 3 Remaining part of tank (c) 4 hours 48 minutes = 96 – 72 = 24 units 45 min 60 min +4 work done 2 minutes 1 unit ¯ ¯ 352 minutes 176 units ´ 176 ´ 176 Remaining part = 180 – 176 = 4 units 3. Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes open Alternately for 2 hours. In how much time B will take to fill the remaining tank? (a) 7 1 hours 2 (b) 2 2 hours 5 (c) 2 2 hours 5 (d) 3 1 hours 3 Time taken by A to fill remaining part = 4 = 1 minute 4 So, total time taken = 352 + 1 = 353 minutes 5 hours 53 minutes Two pipes X and Y can fill a cistern in 24 minutes and 32 minutes respectively. If both the pipes are opened together, then after how much time (in minutes) should Y be closed so that the tank is full in 18 minutes? (a) 10 (b) 8 (c) 6 (d) 5 Pipe and Cistern Sol. (d) According to the question A B 6 4 8 24 (Total Capacity) = 7 units/hour tank filled by A and B in two hours = 7 × 2 = 14 units 1 hours 2 (b) 6hours 1 hours 3 Sol. (d) According to the Question (c) 10hours A 4h B 16h (d) 5 4 16 (Total Capacity) –1 efficiency of A and B = 4 – 1 = 3 units/hour  time taken by A & B to fill the full tank = 5. 16 1 = 5 h. 3 3 Pipe A can fill the tank in 12 hours and pipe B can fill the tank in 8 hours and third pipe C empties tank in 15 hours If all pipes are opened together then after 5 hours what portion of the tank will be filled. (a) 17 24 (b) 24 17 (c) 17 120 (d) 1 3 3 efficiency of A and B = 4 + 3 10 1 = 3 hours. 3 3 A tank has two pipes. The first pipe can fill it in 4 hours and the second can empty it in 16 hours. If two pipes be opened together at a time then the tank will be filled in (a) 5 after 8 minutes it must have closed –3 Time Pipe Y fill the remaining part in 24 = = 8 min 3 So, 180 (Total Capacity) Efficiency of A and B in 2 minutes = 4 – 3 = 1 unit. 4. So, tank filled by X in 18 minutes = 18 × 4 = 72 units  time taken by B to fil l the Remaining part = X would be open till the end. Sol. (d) 2. 96 (Total Capacity) (b) 3 hours 40 minutes (d) 5 hours 53 minutes B 32 min  4 According to the question, (a) 2 hours 55 minutes A 24 min Sol. (a) A B 12 h 8h 10 15 120 (Total Capacity) –8 C 15 h Remaining capacity of tank Efficiency of A, B and C = 24 – 14 = 10 units = 10 + 15 – 8 = 17 units/hour  Total time taken by A & B to Tank filled by A, B and C in 5 hours = 17 × 5 = 85 units  Required portion = 85 17 = 120 24 A tap can fill a cistern in 8 hours and another can empty it in 16 hours. If both the taps are opened simultaneously the time (in hours) to fill the tank is: (a) 8 (b) 10 (c) 16 (d) 24 Sol. (c) Accroding to the question A 8 hr 2 16 (Total Capacity) B 16hr –1 Efficiency of A and B =2–1=1 fill the tank = 9. 6.  Total time taken = (a) 3 15 hours –2 B 10 hours –3 30 (Total Capacity) Total efficiency of A & B = 3 + 2 = 5 units  time taken by A & B to empty the full tank = 8. Two pipes A and B can fill a tank in 30 minutes and 15 minutes respectively. If both the pipe are opened simultaneously, in how much time will be taken to fill the tank? A B 15 min 2 11 (d) 31 19 25 min B 40 min C 30 min –20 600 (Total Capacity) = (24 + 15 – 20) = 19 units/minute  Total time taken fill the tank = 600 11 = 31 min. 19 19 10. Two pipes A and B fill a tank in 36 minutes and 48 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 27 minutes? (a) 10 min (b) 12 min (c) 14 min (d) 16 min A 36min 4 B 48 min 3 30 (Total Capacity) Efficiency of A and B = 1 + 2 = 3 units 144 (Total Capacity) According to the question, A would be opened till the end.  A+B 60 min B+C 40 min C+A 30 min 2 3 120 (Total Capacity) 4 Efficiency of A, B and C +24 +15 Total efficiency of A, B & C (c) 8 minutes (d) 9 minutes Sol. (a) According to the question 1 5 13 Sol. (d) According to the question (a) 10 minutes (b) 12 minutes 30 min (b) 15 Sol. (b) According to the question 30 = 6 hours. 5 A 2 13 2 (c) 8 13 7. A Tap A can fill a water tank in 25 minutes, tap B can fill the same tank in 40 minutes and tap C can empty in 30 minutes. In how much time they completely filled up or emptied the tank? 16 = 16 hours. 1 A pipe can empty a tank in 15 hrs and another pipe can empty it in 10 hours. If both the pipes are opened simultaneously. Find the time in which a full tank is emptied. (a) 8 hrs (b) 6 hrs. (c) 4 hrs. (d) 5 hrs. Sol. (b) According to the question 30 = 10 min. 3 11. Three pipes A, B and C are connected to a tank , A and B together can fill the 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 (a) 80 min, 240 min,48 min (b) 40 min,120 min,24 min (c) 60 min, 250 min, 64 min (d) 65 min,240 min,64 min Sol. (a) According to the question = 4+3+2 = 4.5 units 2 A’s efficiency = 1.5 units B’s efficiency = .5 unit C’s efficiency = 2.5 units Time taken by A = 120 = 80 min 1.5 Time taken by B = 120 = 240 min .5 Time taken by C = 120 = 48 min 2.5 12. Three pipes A, B and C are connected to a tank. A and B together can fill the tank in 12 hrs. B and C together in 20 hrs and C and A together in 15hrs. In how much time will be fill the tank separately? (a) 10 hrs, 15 hrs,30 hrs (b) 20 hrs, 15 hrs, 60 hrs. (c) 20 hrs, 30 hrs, 60 hrs. (d) 20 hrs, 30 hrs, 45 hrs. Sol. (a) According to the question A +B 12 h 5 So, tank filled by A in 27 minutes = 4 × 27 = 108 units B+C Remaining capacity of tank C+A = 144 – 108 = 36 units Pipe B fill the remaining tank in Efficiency of A, B and C = 36 = 12 minutes 3 So, after 12 minutes it must have closed. 20h 3 4 = 60 (Total Capacity) 15h 5 +3 +4 = 6 units 2 A’s efficiency = 3 units B’s efficiency = 2 units C’s efficiency = 1 unit Pipe and Cistern Time taken by A = 60 = 20 hr 3 Time taken by B = Time taken by C = 60 = 30 hr 2 60 = 60 hr 1 13. Two pipes can separately fill a tank in 10 hrs and 15 hrs respectively Both the pipe are opened to fill the tank but when 1 th full a leak 6 develops in the tank through the tank is 1 th of the water supplied 6 by both the pipes leak out. What is the total time taken to fill the tank? which Sol. (a) 7 hrs (b) 5 hrs (c) 6 hrs. (d) 9 hrs (a) A 10 hr 3 B 15 hr 2 30 (Total Capacity) Efficiency of A and B = 3 + 2 = 5 units/hour Time taken by A and B to fill the 1 th part of total capacity 6 Remaining part = 30 – 5 = 25 units  Efficiency of both the pipes when 1 th of total efficiency of leakout 6 æ 1ö 25 ÷= = 5 × çç1 – 6 ÷ units/hour è ø 6 time taken by the both pipes after leaking = 25 = 6 hours 25 6 Hance, total time taken = 6 + 1 = 7 hours. 14. Two Pipes A and B can separately fill a tank in 2 hours and 3 hours respectively. If both the pipes are opened simultaneously in the empty tank, then the tank will be filled in (a) 1 hours 12 minutes Pipe and Cistern A 2hr 3 B 3 hr 2 A 20 min +3 B 30 min –2 Efficiency of A and B in 2 minutes = 3 – 2 = 1 unit Time work 6 (Total Capacity) (A+B) fill the tank in 24 ´ 60 ´ 60 ´ 300 1 × 600 1000 4320000 = = 4320 litres 1000 16. Having the same capacity 9 taps fill up a water tank in 20 minutes How many taps of the same capacity are required to fill up the same water tank in 15 minutes? (a) 10 (b) 12 (c) 15 (d) 18 100 × 1 unit ¯ ¯ 114 minutes 57 units ´ 57 Remaining part of the tank = 1 (24min × 60min × 60sec) × 300 days No of litres wasted = 2 minutes ´ 57 T.C 6 = Efficiency of (A + B) = 3+2 1 = 1 hours 12 min 5 15. A tap drops at a rate of one drop/ sec 600 drops make 100ml The number of litres wasted in 300 days is: (a) 4320000 (b) 432000 (c) 43200 (d) 4320 Sol. (d) 1 sec ––– 1 drop No of second in 300 days. 60 (Total Capacity) = 60 – 57 = 3 units time taken by A to fill the Remaining tank = 3 = 1 minute 3 Hence, total time taken by both the pipes = 114 + 1 = 115 minutes 18. Two pipes A and B can fill a tank with water in 30 minutes and 45 minutes respectively. The third pipe C can empty the tank in 36 minutes First A and B are opened After 12 minutes C is opened Total time (in minutes) in which the tank will be filled up is: (a) 12 (b) 24 (c) 30 (d) 36 Sol. (b) 180 +6 A +4 B –5 1 30 ´ 5 6 = = = 1 hours 5 5 (b) 2 hours 30 minutes (c) 1 hours 15 minutes (d) 1 hours 20 minutes Sol. (a) C 30min 45min 36min tank Filled by (A + B) in 12 min = 12 × (6 + 4) = 12×10= 120 units Remaining capacity of tank = 180 –120 = 60 units After 12 min, emptied pipe C is also opened Sol. (b) é m ´ h ´ t m ´ h2 ´ t 2 ùú 1 1 ê 1 = 2 êë úû w1 w2 9taps ×20mins = Ttaps × 15mins T = 12 Taps 17. 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 for one minute each how soon will the cistern be filled? (a) 121 minutes (b) 110 minutes (c) 115 minutes (d) 120 minutes Sol. (c) So, total capacity of A, B and C = 6 + 4 – 5 = 5 units Time taken by A, B and C with efficiency 5 units to fill the remaining part = 60 = 12 min. 5 Therefore, total time which the tank will be filled up = 12 + 12 = 24 minutes. 19. There are three filling pipes each capable of filling a cistern alone in 8 minutes and 2 emptying pipes each capable of emptying the cistern alone in 10 minutes. All pipes are opened together and as a result, tank fills 7 litres of water per minute. Find the capacity of the tank. Sol. (a) 20 litres (b) 25 litres (c) 40 litres (d) 30 litres pipes are opened together for a certain time but being clogged, 5 only of full quantity of water 6 flows through the former and 8 5 –10 –4 40 Emptying pipe (B) 5 through the latter pipe. 8 The obstruction, however being suddenly removed, the cistern is filled in 5 minutes from that moment. How long was it before the overflow began? Net part of water filled (c) Sol. According to the question :- B 25 min Capacity of the tank (Let both the pipes remain clogged for x minutes) and hence full flow began after x minutes only. In what time would a cistern be filled by three pipes whose 1 cm, 2 3 cm running parallel, when the largest one alone fills it in 61 minutes. The amount of water flowing in through each pipe being proportional to the square of its diameter? (a) 20 min (b) 36 min (c) 18 min (d) 72 min Sol. (b) Note : In such type of questions to save your valuable time follow the given below method. Required time  diameters are 1 cm, 1 2 2 4 2 2 1      2 3   61  4  9 61  4 = 16 9  16  36   1 4 9 = 36 minutes A cistern can be filled by two pipes filling separately in 15 and 25 minutes respectively. Both = = 12 hours 7 A 2 hours B 3 hours A + B +C 5 units/min 75 3 units/min 12 Total capacity ( in units ) 7 units/hr Required time for pipe ( C ) to empty the tank = 23. 75 100 x  45 x = 35 24  145x = 840  x = 840 = 145 168 minutes 29 A tank has three pipes. The first pipe can fill 50% of the tank in 1 hour and second pipe can fill (c) 3 hours Sol. 2 part in 2 hour. The third pipe 3 is for making the tank empty. When all three pipes are opened, 7 part of the tank is filled in 1 12 hours. How much time will the third pipe take to empty the completely filled tank? = 4 hours A bath can be filled by the cold water pipe in 5 hours and by hot water pipe in 7 = 75 25 x 15 x  + 40 = 6 8 12 3 1 hours. A per2 son leaves bathroom after turning on both pipes simultaneously and returns at the moment when the bath should have been full. Finding, however the waste pipe has been left open, he now closes it. In 2 hours more the bath is full. In what time should the waste pipe empty it: (a) 6 hours (b) 4 hours 5 5    5  x + 3× x  +5  5  3 6 8   22. 4 = (6 + 4) – 7 = 3 units/hr Total capacity ( in units ) Part of cistern filled in x minutes + part of cistern filled in 5 minutes = Cistern filled  2 hours 7 6 units/hr Efficiency of waste pipe ( C ) = (15 – 8) = 7 litres/min = Required time for (A+B+ C ) (b) 15 min 7 =  40 = 40 litres 7 21. 148 min. (d) None of these 29 A 2 (b) Required time for pipe A to fill the tank = 2 hours Let C is the empty pipe. 161 168 min. (b) min. 29 29 (a) Efficiency of the two emptying pipes = 4 × 2 = 8 litres/min 61  (d) 6 hours Capacity (litres) Efficiency of the three filling pipes = 5 × 3 = 15 litres/min 20. (b) 4 hours (c) 5 hours Required time for pipe B to fill the tank = 3 hours only (c) Filling pipe (A) Sol. (a) 3 hours A B (d) 4 1 hours 2 (d) Let the cold water and hot water pipes are A and B respectively. 5 hours 3 units/hr 15 Total capacity ( in units ) 15 hours 2 units/hr 2 Required time to fill the bath = 15 3   2  = 3 hours Pipe and Cistern According to the question :Water filled by the pipe (A + B) in 2 hours = Water wasted by waste pipe ( C ) in 3 hours Pipe and Cistern  Efficiency of waste pipe ( C ) 2  (3  2) 10 = = units/hr 3 3 Required time for ( C ) to empty the bath = 15 9 1 × 3= =4 hours 10 2 2