Marriott Corp. yesterday reported a 27 percent increase in profits for the second quarter ended July 19, with earnings per share 25 percent above their level a year earlier.

Second-quarter net income was $21.8 million (81 cents a share) compared with $17.2 million (65 cents) a year ago. Sales rose 19 percent rise to $463.6 million.

Operating income rose 15 percent to $55.4 million for the quarter, a gain that President J. W. Marriott attributed to gains for the company's contract food service, restaurants and theme parks. Based in Bethesda, Marriott operates a growing hotel business, restaurants that include Roy Rogers, Big Boy and Farrell's, and two Great America theme parks. Earnings rose faster than income, the company said, primarily because interest expenses were reduced by the sale last year of three hotels.

Profits for the first half were $36.2 million ($1.35), up from $29.9 million ($1.03) last year. Sales were $876.2 million for this year's first half, up from $739.6 million in the 1980 period.

Virginia National Bankshire Inc. reported record earnings of $6.87 million (95 cents a share) for the second quarter, up from $5.74 million (83 cents) a year earlier.

The Norfolk-based bank holding company also announced an increase in its regular quarterly dividend to 35 cents a share from 30 cents, starting with a payout Oct. 1 to shareholders of record Sept. 4.

Earnings for the first half were $13.75 million ($1.92) compared with $11.71 million ($1.69) last year. Income before securities losses was $14.85 million for the half, up from $11.98 million. In the second quarter along, operating profits were $7.64 million ($1.07) vs. $5.88 million (85 cents).

Company Chairman C. A. Cutchins III attributed the earnings boosts to higher volumes of earning assets and a wider spread between the cost of the money it lends and the interest rate it charged. Assets on June 30 were $2.84 billion, a $290 million increase over last year.

Madision National Bank of Washington, a subsidiary of James Madison Ltd., said net income rose 18 percent for the second quarter to $1.33 million ($3.24 a share) from $1.13 million ($2.75) last year.

Total assets rose 14 percent to $189.3 million, deposits increased 10 percent to $157.5 million, and loans rose 17 percent to $112.4 million.