## Arithmatical - Pipes and Cisterns

DIRECTIONS : Problems based on Pipes&Cisterns.
1. 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 ? A.  2 B.  2.5 C.  3 D.  3.5
Solution
 All the three pipes together will fill the tank in 3 hours. part filled by (A+B+C) in 1 hour = (1/5 + 1/6 + 1/30) ‹=› 1/3.
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 B.  7 hours C.  8 hours D.  14 hours
Solution
 Leak will empty the tank in 14 hours. Work done by the leak in 1 hour =(1/2 - 3/7) ‹=›1/14.

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 B.  80 gallons C.  120 gallons D.  160 gallons
Solution
 [ - ve sigh means emptying] =120 gallons. Work done by the waste pipe in 1 minute =1/15-(1/20+1/24) = (1/15-11/20) = - 1/40 Volume of 1/40 part = 3 gallons. Volume of Whole = (3×40)
4. 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.  7 hrs 30 min B.  7 hrs 45 min C.  8 hrs 30 min D.  8 hrs 45 min
Solution
 Therefore the tank will be full in 15/2 hours Net aprt filled in 1 hour = (1/10+1/12-1/20) = 8/60 = 2/15. ‹=› 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 B.  7960 C.  8290 D.  8640
Solution
 Work done by the inlet in 1 hour = (1/8 - 1/12) = 1/24. Work done by the inlet in 1 min. = (1/24 × 1/60) = 1/1440. Volume of 1/1440 part = 6 litres. Therefore, Volume of whole = (1440×6) ‹=› 8640 litres.
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