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Pipes and Cisterns

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Pipes and Cisterns -> IMPORTANT FACTS AND FORMULAE

Inlet : A pipe connected with a tank or a certain or a reservoir, that fills it, is known as an inlet.
Outlet : A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as an outlet.
I. If a pipe can fill a tank in x hours, then :
part filled in 1 hour = 1 / x.
II. If a pipe can fill a tank in y hours, then :
part emptied in 1 hour = 1 / y.
III. 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, the net part filled in 1 hour = (1/x - 1/y).
IV. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours(where x > y), then on opening both the pipes, the net part emptied in 1 hour = (1/y - 1/x).

Pipes and Cisterns -> SOLVED EXAMPLES

1. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
  Sol. Part filled by A in 1 hour = 1 / 36;
Part filled by B in 1 hour = 1 / 45;
Part filled by (A + B) in 1 hour = (1 / 36 + 1 / 45) = 9 / 180 = 1 / 20.

Pipes and Cisterns -> EXERCISE

1. A pump can fill a tank with a 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 hrs
  • B. 7 hrs
  • C. 12 hrs
  • D. 14 hrs
Ans: D.
Sol.
Work done by the leak in 1 hour = (1/2 - 3/7) = 1/14.
∴ Leak will empty the tank in 14 hrs.
 
2. 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
Ans: D.
Sol.
Work done by the inlet in 1 hour = (1/8 - 1/12) = 1/24.
Work done by the inlet in 1 hour = (1/24 x 1/60) = 1/1440.
∴ Volume of 1/1440 part = 6 litres.
∴ Volume of whole = (1440 x 6) litres = 8640 litres.
 
 
3. 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?
 
  • A. 18
  • B. 15
  • C. 16
  • D. 12
Ans: A.
Sol.
Capacity of each bucket = 9 litres.
Number of buckets needed = (162/9) = 18.