Table of contents 
Introduction: Pipes & Cisterns 
Introduction: Negative Work 
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Example 1. A Cistern has three pipes A, B, and C. Pipe A can fill a Cistern in 10 hrs, Pipe B can fill a Cistern in 5 hrs while Pipe C can empty the Cistern in 20 hrs. If they are switched on at the same time; in how many hours will the Cistern be filled?
Solution:
 In one hour, Pipe A can fill 100/10 = 10% of the Cistern.
 In one hour, Pipe B can fill 100/5 = 20 % of the Cistern.
 In one hour, Pipe C can empty 100/20 = 5 % of the Cistern.
 If all three are working together, (10 + 20 – 5) = 25% of the Cistern will get filled in one hour, so it will take 4 hrs for the Cistern to fill.
Example 2. A tank can be filled by tap A in 6 hrs and by tap B in 3 hrs. But when they are open simultaneously to fill an empty tank, they take 3 hrs more than their normal Time. A hole is later discovered as the reason for the delay. Find the Time taken by the hole to empty the tank if it is completely filled.
Solution:
 Tap A takes 6 hrs to fill, so in one hour it will fill 16.67 % of the tank.
 Tap B takes 3 hrs to fill, so in one hour it will fill 33.33% of the tank.
 Together they will fill 16.67% + 33.33% = 50 % of the tank.
 They should take 100/50= 2 hrs to fill the tank. But they take 3 hrs more, because of the hole; they totally take 5 hrs to fill, i.e. they fill 20% in an hour.
 This is possible if the hole empties 5020 = 30% of the tank in an hour.
 So, to completely empty the full tank, the hole will take 100/30 hrs = 3.33 hrs = 3 hrs and 20 mins.
Example 3. 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?
Solution:
 Part filled by A alone in 1 hour = 1/36
 Part filled by B alone in 1 hour = 1/45
∴ Part filled by (A + B) in 1 hour = Hence, both the pipes together will fill the tank in 20 hours.
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