I'm wondering how it is with fighting the tournament now.
Is it easier/cheaper doing ex. 40 provinces 2 rounds (first 10, 6 rounds) or doing 25 provinces 5 rounds ?
I would say it all depends on what you want out of the tourney.
The easiest/cheapest to play the max number of encounters would be a stairs system: say 22*6 rounds, 23*5 rounds, 24*4 rounds etc all the way to round 6. The reason being that those encounters all have the same difficulty.
But max encounters doesn´t help it is you are after a certain reward. From your 2 examples I would guess that you are only interested in KP.
How many provinces to do in round 2 vs 5 is a rather complex topic. The general fact is as
@FieryArien says expense goes up faster in provinces than over rounds so it will be easier to do 25*5 than 40*2. however there are other factors to be considered. as well and the truth most likely will end up in the middle (but closer to the 25*5), so maybe 30 in round 2 and 20 in round 5?
For example: if you do 40*2, 50% of your encounters give KP (30 out of 60 above the 10 standard), while 25*5 only contains 40% KP rewards (30 out of 75), but of course they give 0.5 KP more. Or in other words you need to fight an extra 15 encounters without KP compared to the alternative. Then there is the randomness of the encounters both in catering resources and enemy troops, that can push you towards skipping a certain province and therefore messing up the "system".
And that is if you completely disregard any other rewards like tourney scores (round 6 is top) or enchantments (round 1 and 4 are good). If you want to consider those, the whole thing gets much more complicated.
As a rule of thumb: Start with the stairs and then makes the steps your interested in larger than the others and you´ll get something that should serve you well.