Marriott Corp., benefitting in particular from a strong hotel business, yesterday reported record sales and profits for the quarter ended Oct. 21.

In other corporate statements yesterday, Capital Mortgage Investments of Chevy Chase, a real estate investment trust, listed a net loss of $3.6 million in the first nine months of 1977 and American Finance System reported a sharp gain in profits for the same period.

For the first quarter of Marriott's new fiscal year, the lodging and restaurant firm reported earnings of $12.95 million (35 cents a share), up 28 per cent from $10.16 million (28 cents) a year ago. Sales rose 15 per cent to $276 million.

President J. W. Marriott Jr. said pretax hotel profits jumped 50 per cent in the quarter on a 22 per cent increase in sales. Five hotels were added in the past year, including two in the quarter, for a total of 36 company-operated units and 15,383 hotel rooms under management.

Pretax profits of restaurant operations rose more than 35 per cent on a 7 per cent sales gain, with Farrell's ice cream parlors profitable for the second consecutive quarter compared with losses last year.

Marriott also said that while attendance at the firm's two amusement parks fell 6 per cent from the 1976 levels in the quarter, revenues were up 12 per cent. Profits of the once-troubled Sun Line cruises more than doubled, he added.

Dart Drug Corp., a Landover-based retail drug chain, reported a 19 per cent jump in profits for the six months ended Sept. 30. Earnings totaled $1.1 million (59 cents a share) on sales of $86 million compared with profits of $903,000 (49 cents) and sales of $82 million a year earlier.

For the second quarter alone, Dart profits rose by 77 per cent to $651,000 (36 cents) on sales of $44 million from earnings of $368,000 (20 cents) and revenues of $42 million last year.

President Herbert H. Haft said the increased earnings reflected higher profits margins on an increased volume. His firm recently opened two large drug stores in Richmond and plans to open more of the 22,000-square-foot units in the current quarter. He said sales generated at Dart's first Crown book store "were strong" and confirmed earlier reports that additional book stores are planned in the current fiscal year.

Capital Mortgage Investments said its net worth has been reduced to a negative $1.7 million as of Sept. 30, in the wake of third-quarter and nine-month losses.

The trust lost $3 million in the quarter compared with a loss of $559,000 in the same period last year; the nine-month loss of $3.6 million contrasts with profits last year of $159,879 (10 cents a share).

CMI said the recent losses reflect an increase in reserves for possible bad loans of $2.75 million in the nine months. During the quarter, CMI closed a new two-year-loan agreement with its 23 bank lenders; since Sept. 30, CMI has accepted bids for $550,000 from three banks to purchase assets in exchange for cancelled debts.

The recent bank accord provides for CMI to issue convertible preferred shares in exchange for cancelling unpaid interest claims. Issuing 238,620 preffered shares requires a reduction in the exercise price of CMI's outstanding warrants from $20 a share to $17.63, the trust added.

American Finance System, a consumer finance company based in Silver Spring, reported third-quarter profits of $1.3 million (27 cents a share) compared with $693,000 (11 cents) a year earlier. Revenues rose to $21.3 million from $20.5 million.

In the first nine months, AFS earned $5.4 million ($1.07) vs. $1.9 million (29 cents), and revenues were unchanged at about $63 million.

The company, which operates 375 consumer loan offices (down from 427 last year), said the 1977 results included one-time gains from tax loss carry forwards of $384,000 in the third quarter and $1.6 million for the nine months.

Loan volume during the first nine months rose $4.7 million to $266 million.

Flow General, Inc., a McLean manufacturer of biological and medical products, reported profits fo $311,000 (21 cent a share) in the first quarter ended Sept. 30, up 34 per cent from $232,000 (21 cents) last year. Sales rose 11 per cent to $11 million.

Fair Lanes, Inc., a Baltimore-based bowling center and restaurant company, reported record earnings of $195,688 (6 cents a share) in the first quarter ended Sept. 30, up from $122,423 (4 cents) a year earlier. Revenues increased 13 per cent to $9.6 million.