Pipes & Cisterns: Formulas & Solved Examples

Pipes & Cisterns uses exactly the same logic as Time & Work — just think of "filling a tank" instead of "doing a job". THE METHOD • If a pipe fills a tank in x hours, in 1 hour it fills 1/x of the tank. • An inlet pipe is POSITIVE (+1/x); an outlet pipe or leak is NEGATIVE (−1/y). • When pipes work together, ADD their one-hour rates; the total time = 1 ÷ (combined rate). SOLVED EXAMPLES 1) Pipe A fills a tank in 6 hours, pipe B in 4 hours. Together? 1/6 + 1/4 = 2/12 + 3/12 = 5/12 per hour → time = 12/5 = 2.4 hours. 2) Inlet fills in 5 hours; a leak empties in 10 hours. Net? 1/5 − 1/10 = 2/10 − 1/10 = 1/10 per hour → 10 hours to fill. EXAM ANGLE: Decide the sign first (filling +, emptying −), add the rates, then invert for time. Watch for "half-full" or "first opened later" twists. Practise pipes & cisterns sets on Govt Exam Center.