xcraft:
the landlord ... doesn't want to waste any money.
Yes, wires dipped into water that is not pure will provide enough conductivity for you to detect. It's unlikely that dirty water that has then been drained through the structure of the building would ever be pure, but if you did run the same test with de-ionised water the conductivity would be much lower.
And your landlord may not want to waste money, but he still has an obligation to prevent the leak not just to 'fix' it every time it happens (in most countries, this would be a legal obligation not just a moral one). Obviously his interests are opposed to yours - he just wants a quiet life and as much profit as he can get away with - but you do have the right to require him to actually fix the problem. He does not have the right to make you endure water leaks for months or perhaps years until some third party decides to move out. If it costs him money, that's his problem not yours. He's running a business, this gives him certain responsibilities, fixing problems like this is one of them.