The Washington Post Co., hit by a slump in advertising, reported yesterday that its profits fell 12 percent in 1990 and 18 percent in the fourth quarter.

For the year, the company earned $174.6 million ($14.45 per share), compared with $197.9 million ($15.50) in 1989. In the fourth quarter, the company earned $42.1 million ($3.55 per share), compared with $51.1 million ($4.06) in the year-earlier period.

In a statement, The Post Co. said its results "reflected the weakening national economy and soft advertising environment." The ad slump has depressed the performance of almost all major media companies, especially during the fourth quarter, which is typically the busiest season of the year in terms of advertising.

The company's 1990 sales were $1.44 billion, essentially flat from 1989. Fourth-quarter sales were down 3 percent to $369.4 million.

The Post Co.'s fortunes were reflected in its largest property, The Washington Post. The newspaper's advertising volume declined 12 percent during the year and 17 percent in the fourth quarter. For the year, The Post's advertising sales were $535.9 million, off 7 percent from $574.4 million in 1989.

Total newspaper operating profit, which includes those of The Herald in Everett, Wash., declined 19 percent to $143.8 million from $176.6 million in 1989.

Newsweek magazine's operating profit decreased 5 percent to $26.9 million on revenue of $340.2 million during 1990. The revenue figure represented a 2 percent increase over 1989.

The company's broadcast division, which includes television stations in Detroit, Miami, Hartford and Jacksonville, Fla., reported annual operating income of $68.9 million, a 4 percent drop, on sales of $179.4 million, down 2 percent from 1989.

The company's cable television division registered a 12 percent gain in operating profit and a 12.5 percent increase in revenue last year. Revenue was $145.5 million and operating income totaled $29.2 million.