Introduction
Pipes & Cisterns is simply Time & Work applied to filling/emptying a tank — the exact same
efficiency method from Chapter 13 works here, with one key twist: outlet (emptying) pipes count
as negative work.
Core Setup
Flowchart — Inlet vs Outlet Efficiency
Inlet Pipe (fills tank) → Positive efficiency
Outlet Pipe (empties tank) → Negative efficiency
Take Total Work = LCM of all given times (same as Time & Work), then combine efficiencies with correct signs.
Q. Pipe A can fill a tank in 10 hours and Pipe B can empty it in 15 hours. If both are opened together, how long will it take to fill the tank?
Total Work = LCM(10,15) = 30 units
A's efficiency = +30/10 = +3 units/hr; B's efficiency = −30/15 = −2 units/hr
Combined efficiency = 3−2 = +1 unit/hr
Time to fill = 30/1 = 30 hours
Three Pipes Together
Q. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. A third pipe C can empty it in 15 minutes. If all three are opened together, find the time to fill the tank.
Total Work = LCM(20,30,15) = 60 units
A = +60/20 = +3; B = +60/30 = +2; C = −60/15 = −4
Combined = 3+2−4 = +1 unit/min
Time = 60/1 = 60 minutes
"Pipe Opened for Part of the Time" Pattern
Q. Pipe A can fill a tank in 12 hours. Pipe B can fill it in 15 hours. Both pipes are opened together, but Pipe A is closed after 4 hours. In how many more hours will the tank be filled by Pipe B alone?
Total Work = LCM(12,15) = 60 units
A's rate = 5/hr, B's rate = 4/hr
Work done in first 4 hrs (both open) = (5+4)×4 = 36 units
Remaining work = 60−36 = 24 units, filled by B alone at 4 units/hr
Time = 24/4 = 6 more hours
Leak in the Tank Pattern
💡 Standard Approach: A "leak" is simply another outlet pipe — treat it exactly like an emptying pipe with negative efficiency, and combine it with the filling pipe(s) the same way.
Q. A pipe can fill a tank in 6 hours. Due to a leak, it takes 8 hours to fill. In how many hours can the leak alone empty the full tank?
Total Work = LCM(6,8) = 24 units
Pipe's rate = +4/hr; combined (with leak) rate = 24/8 = +3/hr
Leak's rate = 4 − 3 = 1/hr (emptying)
Leak alone empties the tank in 24/1 = 24 hours
✅ Practice Focus: Sign convention — inlet positive, outlet/leak negative · LCM-based efficiency method (identical to Time & Work) · Pipe closed/opened partway through pattern · Leak-in-tank problems treated as a hidden outlet pipe.