Marriott Corp. and the Student Loan Marketing Association have announced sharp increases in profits for the first quarter.

Marriott Corp. said its first-quarter net income climbed 20 percent to $27.7 million ($1.04 a share), compared with $23 million (83 cents) during the same period last year.

Revenue for the food and lodging chain jumped 18 percent to $874.2 million, compared with $743.9 million during the first three months of 1984.

"We are off to a strong start in 1985, and we feel very good about our overall prospects for the year," said Marriott President J. W. Marriott Jr.

Marriott attributed the higher earnings to increased traveling and the addition of two new food-service subsidiaries, Toledo-based Gladieux Corp. and Buffalo, N.Y.-based Service Systems Corp.

The Student Loan Marketing Association reported that its first-quarter net income was up 33 percent to $28.9 million (56 cents), compared with $21.6 million (41 cents) during the same period last year.

"Sallie Mae's strong first-quarter performance resulted primarily from solid growth in the corporation's loan assets in combination with Sallie Mae's continued success in cost-effectively funding its operations," said Edward A. Fox, president of Sallie Mae.

Sallie Mae, which buys insured student loans from lenders, purchased $577.7 million in the first quarter, up 51 percent from $383.2 million in the first quarter last year.

As of March 31, Sallie Mae's total portfolio of purchased student loans was $5.9 billion, 23 percent higher than at the close of the 1984 first quarter.