CAT Quant · Chapter Test
Pipes & Cisterns — 25-Question Test
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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
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