How should we split $2,000 rent fairly with $62k vs $37k incomes?

One brings in $62K and the other brings in $37K. They don't want a joint bank account, and they don't touch one another's money (We can already predict how things are going to go in the future, but w. e.) For now let's pretend it will work between them, and the rent is $2,000.

I'm saying that if each contribute around 2% of their salary towards rent, the one with 62K pays $1,200 and the 37K pays $800. That way the expense has the same, damn close, strenuous % effect on their income.

But one of them don't agree... What do you think?

I like your idea of 2% each.
I don't like your idea. It should be 50/50.
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How should we split $2,000 rent fairly with $62k vs $37k incomes?
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