Quality Inns International, the Silver Spring lodging chain, yesterday reported a dramatic turnaround in its operations and the best third quarter profits in the company's history.

For the three months ended May 31, Quality Inns earned $2.53 million (96 cents per share) on sales of $15.6 million, contrasting with a loss of $70,000 (3 cents per share) on sales of $13.7 million in the prior year.

For the first nine months of the company's fiscal year, Quality Inns earned $742,00 (28 cents per share) against a loss of $1.76 million to $41.4 million.

Sharply improved operating results for the company's U.S. inns, which showed a $1.3 million loss for the nine-months last year, but produced more than $1 million in profits this year. Third quarter operating earnings climbed from $416,000 to $1.48 million.

A $2.49 million gain on the sale of two properties, in Kansas City, Mo., and Ratingen, Germany. That gain was offset in part by a $519,000 write-down on another hotel that the company plans to sell below its book value.

A third quarter gain of $226,000 on translation of business in foreign currencies into dollars. Because of the steadily declining value of the dollar against the West German mark, the company's German operations had cost hundreds of thousands of dollars incurrency translation losses.

Sale of the German hotel will largely eliminate those losses in the future, and disposal of unprofitable inns in th's country - including the unspecified property forwhich the half million writedown was taken - should indicate improved future earnings, company sources indecated .