Manor Care Inc. yesterday announced profits of $5.93 million (34 cents a share) for its first quarter ended Aug. 31 compared with profits of $3.57 million (24 cents) in its first quarter a year earlier.

Manor Care, a health care and lodging firm based in Silver Spring, said revenue declined to $88.75 million from $92.3 million between the 1982 and 1983 quarters, mainly because of the sale of 13 nursing centers as well as industrial companies unrelated to the corporation's main activities.

Manor Care owns Quality Inns, a major hotel chain that owns, operates or franchises 470 hotels with 55,625 rooms. It also operates 103 health care facilities that have a total of 13,039 beds.

Shareholders at yesterday's annual meeting authorized an increase in Manor Care common stock from 20 million to 40 million shares. Stewart Bainum Jr., vice chairman of the board, said the company has split its stock twice in the last year. The company may want to split again and the increased authorization of shares will permit the company to do so, Bainum said.

Manor Care has no intention now of making a new issue of stock, but the authorization of 40 million shares gives the company the "flexibility" to do so if it wants to, he added.