In Jakarta, we have far too many cats everywhere, so it would seem that we would not have many rats. However, the rats marginally outnumber the cats, as the cats prefer to eat off the rubbish heaps, while the rats content themselves by eating from my larder and my table. Only the snakes (mainly cobras) do somewhat keep the rats in check, but they make lousy pets.
I heard only about 25% of cats will actually go after rats.