Hotel Investors Trust and Hotel Investors Corp. yesterday reported a decline in profits fo the first fiscal quarter ended Nov. 30. D.C. National Bank, meanwhile, posted a 63 percent increase in earnings during 1980.

The Chevy Chase-based hotel investment trust and the separate hotel property leasing firm, which are paired and traded as a unit on the American Stock Exchange, said first-quarter earnings dipped to $1.4 million (74 cents a share) from $1.5 million (87 cents) a year earlier.

In the prior year, a gain of 23 cents a share from selling a Tallahassee, Fla., hotel increaed net income by $390,000. Not counting that one-time gain, first-quarter operating profits increased to $1.4 million from $1.1 million for a 15 percent increase in per-share earnings to 74 cents from 64 cents.

The Hotel Investors board also declared a regular quarterly dividend of 65 cents a share, payable Jan. 30 to owners of record Jan. 16.

D.C. National Bank reported a 63 percent increase in earnings in 1980. The bank said that earnings climbed from $1.16 million ($5.67 per share) in 1979 to $1.9 million ($9.22).

According to the bank, it was the third consecutive year in which earnings increased by more than 50 percent from the previous year. The bank also reported that deposits increased by 33 percent.

With assets of $137.5 million, D.C. National Bank is the city's seventh-largest bank.

The bank has put a celing on its prime rate of 18 percent, s it did in spring of 1980. "In an economy like ours locally, it is difficult to justify a prime rate any higher," said President Thomas S. Condit.

VSE Corp. of Alexandria reported a drop in after-tx net income of more than 50 percent for the nine months ended Sept. 30. The corporation and its subsidiaries reported consolidated earnings of $336,000 (92 cents a share) for the nine-month period ended compared with earnings of $680,000 ($1.85) for the same period in 1979.

Consolidated gross revenues for the first nine months of 1980 were $31.61 million compared with revenues of $26.491 million for the same period in 1979.