What is the ruling on a seller selling a commodity—which he bought for fifty dinars in cash—to a buyer for sixty dinars on credit, so that the buyer can sell it for fifty dinars in cash to obtain money?

What you have asked about is called Murabaha sale, and it is permissible if the price of the commodity and the profit margin are declared, provided that the buyer sells the commodity to another party. However, if you were to buy it back from him in cash for a lesser amount than what you sold it for on credit, this is called 'Inah sale, which is forbidden due to the Prophet's (peace be upon him) saying: "If you engage in 'Inah transactions, and follow the tails of cattle, and are content with agriculture, and abandon jihad, Allah will inflict humiliation upon you which He will not remove until you return to your religion." The 'Inah sale is when one sells something for a deferred price and then buys it back for a lesser price in cash. This collusion invalidates both transactions.