Washington Corp., a Chevy Chase real estate investment and development firm, reported that profits dipped slightly in 1985, but also that it will declare its first dividends since 1975.

Classic Corp. suffered second-quarter losses, and James Madison Ltd. reported an increase in earnings.

Washington Corp. showed net earnings of $1.1 million (51 cents a share) compared with $1.3 million (54 cents) in 1984.

William N. Demas, Washington Corp.'s chairman, said the company will pay a dividend of 10 cents a share to shareholders of record on Feb. 11. In recent years, the company said it had been retaining all of its earnings for future investment.

*Classic Corp., a Jessup, Md., manufacturer of waterbeds, reported continuing red ink in the fiscal 1986 second quarter. The company said it lost $43,000 (2 cents a share) in the three months ended Dec. 31 compared with a profit of $329,000 (17 cents) in the same period a year ago.

For the year to date, the company said its net loss was $335,000 (17 cents) compared with net income of $515,000 (27 cents) in the first six months of the 1985 fiscal year.

Sales for the year to date totaled $20.5 million compared with $19.5 million in 1985, Classic said.

*James Madison Ltd., the holding company of Madison National Bank of Washington, reported that earnings rose 30 percent in 1985 -- from $2.8 million ($2.28 a share) to $3.7 million ($2.96).

Net earnings for the fourth quarter of the year also rose, from $962,742 (78 cents) in 1984 to $1 million (85 cents), the bank said.

Total assets stood at $353.1 million at the end of 1985 compared with $300.5 million at the end of the previous year, an increase of 17.5 percent.