## Math Topic - Pipes & Cisterns

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PBI Important facts and formulae PBI INSTITUTE 1. 2. 3. 1. Inlet : A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet. Outlet : A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet. If a pipe can fill a tank in x hours, then : part filled in 1 hour — I. If a pipe can empty a tank in y hours, then : part emptied in 1 hour = Il. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part filled in 1 hour = (1 / x- 1 / y)• Ill. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part emptied in 1 hour EXERCISE Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open,in how many hours will the tank be filled ? B. 2.5 D. 3.5 Solution part filled by (A+B+C) in 1 = (1/5 + 1/10 + 1/30) hour 1/3. All the three pipes together will fill the tank in 3 hours. 2. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in A. 5 hours C. 8 hours Solution Work done by the leak in 1 - 3/7) B. 7 hours D. 14 hours hour < = > 1/14. Leak will empty the tank in 14 hours. 3. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is A. 60 gallons C. 120 gallons Solution Work done by the waste pipe in minute 1 B. 80 gallons D. 160 gallons = 1/15 - (1/20+1/24)
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PBI Volume of 1/40 part Volume of = (1/15 - 11/20) - 1/40 = 3 gallons. PBI INSTITUTE [ - ve sigh means emptying] Whole 4. = 120 gallons. Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours.lf all the three pipes operate simultaneously, in how much time will the tank be filled? A. 7 hrs 30 min C. 8 hrs 30 min Solution Net aprt filled in 1 hour B. 7 hrs 45 min D. 8 hrs 45 min = (1/10+1/12-1/20) = 8/60 = 2/15. Therefore the tank will be full in 15/2 hours 7 hrs 30 min. 5. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold ? A. 7580 c. 8290 Solution Work done by the inlet in 1 hour Work done by the inlet in 1 min. Volume of 1/1440 part = 6 litres. Therefore, Volume of whole B. 7960 D. 8640 = (1/8 - 1/12) = 1/24. = (1/24 x 1/60) = 1/1440. 6. 8640 litres. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes ? A. 5/11 c. 7/11 Solution Part filled by (A + B + C) in 3 minutes Part filled by C in 3 minutes Required ratio - 6/11. B. 6/11 D. 8/11 = 3(1/30+1/20+1/10) = 11/20. = 3/10. 7. Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank ?
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PBI PBI INSTITUTE A. C. Solution 8 hrs 18 hrs B. D. 9 hrs 36 hrs Part filled by hour = (1/5 + 1/20) — 1/4. So, A and B together can fill the tank in 4 hours. Work done by the leak in 1 hour = (1/4 - 2/9) = 1/ 36. Therefore, Leak will empty the tank in 36 hrs. 8. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank ? A. 12 min C. 25 min Solution Part filled by A in 1 min Part filled by B in 1 min Part filled by (A+B) in 1 min B. 15 min D. 50 min = 1/20. = 1/30. = (1/20 + 1/30) = 1/12. Both the pipes can fill the tank in 12 minutes. 9. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in A. hours C. hours Solution Net part filled in 1 hour Therefore, the tank will be full in 60/17 hrs. B. hours D. 4x1/2 hours = (1/5 + 1/6 -1/12) = 17/60. 3x9/17 hrs. 10. 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? B. 15 D. 18 c. 16 Solution Capacity of the tank Capacity of each bucket Number of buckets need ed = litres = 162 litres. = 9 litres. = (162/9) 18. Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes 11. 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?
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PBI B. D. PBI INSTITUTE 100 min 120 min A. C. Solution 90 min 110 min Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min. 12. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ? A. 4.5 hrs C. 6.5 hrs Solution Net part filled in 1 hour B. 5 hrs D. 7.2 hrs = (1/4 - 1/9) = 5/36. Therefore,the cistern will be filled in 36/5 hrs i.e, 7.2 hrs. 13. 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. 3 hrs 15 min C. 4 hrs Solution Time taken by one tap to fill half the tank = Part filled by the four taps in 1 hour = (1 - 1/2) Remaining part = 1/2. Therefore, B. 3 hrs 45 min D. 4 hrs 15 min 3hrs. = 2/3. 2/3 : 1/2 : : 1: x (1/2x1x3/2) 3/ 4 hrs i.e 45 mins. So, total time taken = 3 hrs 45 min. Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are 14. opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ? A. 4 hrs C. 7 hrs Solution A's work in 1 hour B's work in 1 hour = 1/6. = 1/4. (A+B)'s 2 hour's work when opened alternately B. 5 hrs D. 9 hrs = 5/12.
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PBI (A+B)'s 4 hour's work when opened alternately Remaining part Therefore, total tank to fill the tank PBI INSTITUTE = 10/12 = 5/6. = (1 - 5/6) = 1/6. (4+1)hrs = 5 hrs.

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