🗺️ Chapter Roadmap
1 Connection with Time & Work
Pipes & Cisterns problems are exactly like Time & Work (Chapter 10). The only difference is the vocabulary:
2 Inlet vs. Outlet
In Time & Work, everyone usually helps to finish the job. In Pipes & Cisterns, one pipe might be filling while another is emptying (Negative Work). This is the "Cistern Twist".
💧 Inlet Pipe (Positive)
A pipe that fills the tank. We treat its work as (+) Plus.
🕳️ Outlet Pipe / Leak (Negative)
A pipe that empties the tank. We treat its work as (−) Minus.
3 The "Two Pipes" Shortcut
If two inlet pipes are filling a tank together, use the Product / Sum rule to find the time taken:
x = Time of Pipe A | y = Time of Pipe B
4 The Leakage Logic
What if Pipe A is filling the tank in x hours, but a Leakage (Pipe B) is emptying it in y hours? To find how long it takes to fill the tank with the leak open, use the Product / Difference rule:
(Divide the product by the difference of their times)
📝 Real Exam Example:
"Pipe A fills a tank in 4 hours. However, due to a leak at the bottom, it takes 6 hours to fill. How long would the leak take to empty a full tank alone?"
5 Net Work Method (3+ Pipes)
If there are three or more pipes, shortcut formulas become complicated. It is better to find the 1-Hour Work for each pipe and then solve using the "LCM method":
The Logic:
1. 1st Pipe Work (+) = 1x
2. 2nd Pipe Work (+) = 1y
3. Leakage Work (−) = 1z
Total 1-Hour Net Work = 1x + 1y − 1z