The Washington Post Co. reported yesterday its net income increased 60 percent last year to $52.4 million ($3.70 a share) from $32.7 million ($2.32) in 1981.

Revenues for the publishing and broadcasting company were up 6 percent to $800.8 million from $753.4 million for the previous year.

Most of the Post Co.'s gains came from its newspaper division, which reported an 84 percent increase in pretax operating income to $57 million from $31 million. Besides The Washington Post, the division publishes The Everett (Wash.) Herald and owns Robinson Terminal Warehouse Corp. of Alexandria.

In 1981, the firm's earnings were held down by losses on Inside Sports magazine and The Trenton (N.J.) Times, and the expense of sharp circulation increases after the close of The Washington Star. The Trenton paper was sold in late 1981 and Inside Sports was sold last year.

In a statement, Chairman Katharine Graham and President Richard D. Simmons said, "Continued efforts to enhance editorial products, improve service to advertisers and strengthen operating management produced good results in 1982, despite the recession. We believe the company is well positioned to maintain its momentum in 1983."

In 1982, newspaper revenues increased 12 percent to $414 million from $368 million, but overall advertising lineage at The Washington Post declined 1.5 percent to 101.6 million lines and classified advertising lineage was down 6 percent.

The Post's circulation as of Sept. 30 was up 16 percent daily to 726,000 and gained 14 percent on Sunday to 972,000.

Lead by strong performances of WDIV in Detroit and WPLG in Miami, operating income of the company's four television stations rose 30 percent to a record $32.1 million from $24.6 million. Revenues were up 16 percent to $104 million from $90 million.

Newsweek magazine's operating income slipped 4 percent to $13.3 million from $13.9 million, and revenues were down 5 percent to $279 million from $294 million as advertising pages in domestic editions fell from 3,106 to 2,847. Newsweek's circulation rose 2 percent to more than 3 million.

In the fourth quarter, Post Co. earnings increased 23 percent to $22.2 million ($1.57) from $18.1 million ($1.28), while revenues gained 3 percent to $224.8 million from $218.1 million the previous year.