Pipes & Cisterns : Rules

Pipes & Cisterns


Pipes and Cisterns problems are similar to Time and Work problems. The main idea is to calculate the work done in 1 hour.


Rule



  • Filling Pipe = (+) Positive Work

  • Emptying Pipe / Leakage = (−) Negative Work


Main Formulas


1. Filling a Tank : If a pipe fills a tank in T hours: Work done in 1 hour = 1/T​​


2. Emptying a Tank : If a pipe empties a tank in T hours: Work done in 1 hour = −1/T​​


3. Multiple Pipes Working Together : 1-hour work = Sum of filling rates − Sum of emptying rates​


4. Total Time : Time = Total Work / Work Done Per Hour​​, For one complete Tank : Total Work = 1​


Therefore: Time = 1 / Net Work per Hour​​


Trick: i. Fill → + , ii. Leak → −


Ex: A pipe fills a tank in 6 hours and another pipe fills it in 3 hours.


1 - hour work = 61​+31​=61​+62​=63​=21​


So, time required: 1/1.5​ = 2 hours , (Note 1.5 = 1/2)​


Note: i. Filling = Add (+),  ii. Emptying = Subtract (−)

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