UP Police SI Pipes & Cisterns

If a pipe fills a tank in 'n' hours, it fills 1/n part in 1 hour. This is the pipe's rate of work. When pipes work together, ADD their rates. For outlet pipes, SUBTRACT their rates from inlet rates.

The combined rate tells you the net filling or emptying speed

- Pipe Rate = 1/Time taken to fill/empty alone - Combined Rate = Sum of individual rates (+ for inlet, - for outlet) - Time with combined rate = 1/Combined rate - Work done = Rate × Time

Take LCM of all individual times. This becomes tank capacity. Each pipe's rate becomes LCM/individual time. This eliminates fractions completely and makes calculations super fast

If two pipes work alternately starting with first pipe, and their individual times are a and b hours, then cycles needed = Total work/(work in 2 hours) and check remainder. The #1 Most Common Trap: Students forget to make outlet pipe rates NEGATIVE. They add all rates as positive and get wrong answers

Inlet = +, Outlet = -, then calculate combined rate. Another major mistake is not converting 'part of tank filled' back to actual time. If question asks when tank will be full and you calculated rate, don't forget the final division step.