First-quarter profits of the Washington Post Co. plunged 54 percent of $1.8 million (13 cents a share) from $3.9 million (27 cents) in the same period a year ago, the company reported yesterday.

The company blamed the first-quarter decline on higher interest expenses and on losses of two new ventures started last year -- Inside Sports magazine and Post-Newsweek Productions, a television programing company.

Revenues for the three months ending March 29 increased by $14.6 million over the first quarter of 1980 to $165.8 million. Revenues increased 13 percent at the newspaper division, which publishes The Washington Post, The Trenton (N.J.) Times and The Everett (Wash.) Herald, and were up 7 percent in the broadcasting division and 6 percent in the magazine division.

Operating income for the quarter fell from $8.7 million to $4.7 million; the newspaper division posted higher operating income, but there were declines in the magazine and broadcasting divisions due to their new ventures.

Advertising linage was off at the company's two biggest publications -- The Washington Post and Newsweek -- "reflecting current economic conditions," the company reported. Display advertising in The Washington Post continued to increase, along with the newspaper's circulation, but classified ad volume fell 6 percent, resulting in an overall decline of about 1 percent. Newsweek's number of advertising pages fell about 10 percent.

Two other factors affected earnings for the quarter, the Post company said. The company's share of affiliate operations produced a loss of $67,000, down from $985,000 last year, because of lower losses at the Bear Island Paper Company. Interest expenses jumped from $2,000 a year ago to $1.3 million because of higher rates and increased borrowing, much of it to finance The Washington Posts's new Springfield printing plant.