We are given:
100 cats kill 100 rats in 100 days.
Let’s understand what this means:
It implies that 1 cat kills 1 rat in 100 days.
Now, we need to find out in how many days 4 cats would kill 4 rats.
If 1 cat kills 1 rat in 100 days, then 4 cats can kill 4 rats in the same 100 days because:
Each cat works independently, and each cat is responsible for 1 rat.
Hence, \[
\boxed{100 \text{ days}}
\]