What is the ruling on investing money with a friend who buys goods with it and sells them, then returns the money with a profit after a few days, with the profit margin being variable based on the ease of sale and the percentage of the capital?

If the agreement is for the profit to be a percentage added to the capital, varying according to the trade's condition, then this is not permissible. This is because guaranteeing the capital, or guaranteeing an additional profit on it, even if variable, invalidates the partnership (sharika) and the mudaraba (profit-sharing partnership). The transaction would then devolve into a guaranteed loan that yields benefit, thus becoming riba (usury). However, if the agreement is for a known, undivided share of the profit, should it occur, with the capital owner bearing the loss of the capital and the mudarib (working partner) bearing the loss of his effort, then this is a valid and Islamically permissible mudaraba.