Is the sale and purchase of used cars Islamically permissible in a situation where the shop owner does not own the cars but acts as an intermediary between the seller and the buyer, taking a percentage or a sum of money in return?

The shop owner here is a broker who mediates between the seller and the buyer for a fee. There is no objection to the broker taking a fee for his work. A condition for the validity of his fee is that it must be known. Therefore, it is not permissible for it to be a percentage of the selling price if that price is unknown to both parties at the time of the brokerage contract, because in such a case, it would be an unknown ju'ala (commission for a specific task), and the Prophet, peace and blessings be upon him, forbade hiring a worker until his wage is made clear to him. Some scholars, however, have permitted the fee to be a percentage. According to the view that the contract is invalid, the fee due to the broker would be the customary wage (ajrat al-mithl).