The Washington Post Co. yesterday reported its 1985 profits grew to $114.3 million ($8.66 a share) including a one-time gain of $12.3 million (93 cents) from the sale of some of its cellular mobile telephone and cable television interests.

Compared with 1984 earnings of $85.9 million ($6.11), the Post Co. showed a 19 percent increase in profits before the sale of assets, to $102 million ($7.73). It had a 33 percent increase in earnings including the one-time gain.

Revenue for the year totaled $1.08 billion, up 9.6 percent from $984.3 million in 1984.

Fourth-quarter income fell 6 percent to $32.5 million from $34.6 million, but earnings per share increased to $2.53 from $2.47 because the company repurchased about 1.1 million shares of Class B common stock. Revenue for the fourth quarter grew 2.7 percent to $291.4 million from $283.6 million.

Annual operating income of the newspaper division was up 21 percent to $114.5 million from $94.6 million, and revenue was up 8 percent to $556.1 million from $516.6 million. Advertising volume at The Washington Post was up 4 percent to 5.46 million inches, and the paper's ad revenue rose 9.2 percent for the year. For the fourth quarter, newspaper division revenue grew 7 percent, while Washington Post advertising increased 3.2 percent to 1.5 million inches from 1.45 million.

Newsweek magazine's operating income for the year was up 31.8 percent to $29.1 million from $22 million despite a 1.7 percent drop in revenue to $326.1 million from $331.6 million in 1984. Newsweek's fourth-quarter revenue fell 12.5 percent, and advertising pages for the quarter were down to 837 from 1,056 in the same period a year ago.

Broadcasting division operating income rose from $50.8 million in 1984 to $57.9 million, after deducting $3.3 million in program development costs. Revenue of the Post Co.'s television operations increased 13.6 percent to $154.5 million from $136 million in 1984. Fourth-quarter TV revenue was up 9.2 percent.

For the first time, the company reported separate results from its diversification efforts, which include cellular radio operations in Miami, Legi-Slate Inc. and the Stanley H. Kaplan Educational Centers. These "other businesses" reported operating income of $3.7 million on revenue of $42 million.

The Post Co.'s equity in earnings of affiliates produced a gain of $4 million for the year compared with a loss of $5.7 million in 1984. The swing came from substantially lower losses from SportsChannel -- a cable TV sports service -- and improved results at the company's newsprint mills. Also included in earnings of affiliates is the Washington Post Co.'s 20 percent interest in Cowles Media Co., publisher of The Minneapolis Tribune.