Introduction
Pipes & Cisterns is Time & Work applied to filling and emptying a tank. An inlet pipe
fills the tank (positive efficiency); an outlet pipe drains it (negative efficiency). The same
LCM-based efficiency method from the previous chapter applies directly.
Core Approach
1. Total capacity = LCM of all given times.
2. Inlet pipe efficiency = +Capacity/its time. Outlet pipe efficiency = −Capacity/its time.
3. Net efficiency = sum of all efficiencies. Time to fill/empty = Capacity ÷ Net efficiency.
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?
Capacity = LCM(10,15) = 30 units. A's rate = +3 units/hr. B's rate = −2 units/hr. Net rate = +1 unit/hr.
Time to fill = 30/1 = 30 hours.
Q. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. Both are opened together, but A is closed after 5 minutes. Find the total time to fill the tank.
Capacity = LCM(20,30) = 60. A's rate = 3/min, B's rate = 2/min. Combined rate for 5 min = 5×3+5×2 = 25 units filled.
Remaining = 60−25 = 35 units, filled by B alone at 2/min → 35/2 = 17.5 min.
Total time = 5 + 17.5 = 22.5 minutes.
⚠️ Key Insight: Always assign a negative sign to outlet (draining) pipes when calculating net
efficiency — forgetting the sign is the most common error in this chapter.
✅ Practice Focus: Combined inlet-outlet net efficiency · One pipe closed partway through ·
Leak-in-the-tank problems (tank takes longer to fill due to a leak).