How much time a cat can live with acute kidney disease when not treated?
PS: For people who will say that I have to treat it (and they have reason) , it's not my cat I'm just asking.
A lot of it depends on if it is acute kidney failure in isolation, or acute-on-chronic. If it's in isolation (i.e. something reversible has caused the renal failure, such as toxins, infection, or dehydration, but the cat does not actually have underlying kidney disease), then often reversing the cause can reverse much of the damage, and a cat in that case might make a full recovery.
However, if the underlying cause is not treated and it's not something the cat can overcome on its own, then the cat likely won't live long.
Acute on chronic is something of a different story, because in that case the cat would already have underlying kidney damage and would be less likely to recover. Also, sometimes untreated acute kidney disease can cause damage that leads to chronic disease.
I wasn't able to find a specific number of how long survival could be expected, suggesting that it's variable. But it could be as little as a few days. Maybe more in some cases.