Module 1 · Arithmetic
Chapter 9: Pipes & Cisterns
Arithmetic
3 topics
What this chapter covers
The 3 topics below make up Pipes & Cisterns on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
📚 Study this chapter
Notes, worked examples and hint-guided practice for every topic.
Start learning →
🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
Practice by topic →
📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
Take chapter test →
Formula Reference Sheet
This chapter
Core rates & capacity
| Tank capacity (smart units) | LCM of all the given fill/empty times |
|---|---|
| Rate of a pipe | Capacity ÷ time = units per hour |
| Pipe filling in x hours | rate = 1/x of tank per hour |
| Net rate (signed sum) | Σ inlet rates − Σ outlet rates |
| Time to fill / empty | Capacity ÷ |net rate| |
CAT power-tools
| Two inlets A (a h) & B (b h) together | time = ab/(a+b) hours |
|---|---|
| Inlet a h with outlet b h (b > a) | time = ab/(b−a) hours |
| Leak empties full tank in L h | leak rate = −1/L tank per hour |
| Inlet fills in x h, leak makes it x+d | leak alone empties in x(x+d)/d h |
| Part filled in t hours | net rate × t (as a fraction of the tank) |
CAT reference
🖩 Graphing Calculator