What is the ruling on two people agreeing to purchase a house, where the first pays 10% and the second pays 90%, then the first person pays the second annual installments that gradually increase his ownership, with the house's rent being divided according to the changing ownership percentage? And is it permissible for the owner whose share is increasing to be the one who benefits from dwelling in the house, paying the other his remaining share of the rent?

There is no objection to dealing with a diminishing partnership (musharakah mutanaqisah). This occurs when two individuals purchase a house with one of them promising to buy the share of the other in stages. It is stipulated that the promise must be non-binding, and the sale of each share must take place at market price on the day of sale, with separate contracts. The rent should be divided according to the shares. It is permissible for one partner to rent the share of the other, with each being responsible for basic maintenance in proportion to their share, and the joint ownership should be registered in a contract to preserve rights.