Quality Inns International Inc. yesterday reported a 24 percent profits rise for the 1980 fiscal year as its chief executive predicted that the expansion of the company's budget motel operation leaves the company in a cautious but optimistic state for the coming year.

The Silver Spring-based company reported 1980 fiscal year profits of $5.4 million ($2.06 a share), up from $4.3 million ($1.63) for the 1979 fiscal year. Revenues rose from $62.04 million to $66.39 million.

Fourth-quarter profits dropped slightly to $1.5 million (57 cents) from $1.63 million (62 cents) a year earlier as revenues rose from $17 million to $18.2 million. The company said the fourth-quarter profits decrease was a result of an increase in its effective tax rate to 39 percent during fiscal 1980 from 25 percent last year.

In other reports, United Virginia Bankshares Inc. reported third-quarter profits of $8.4 million ($1.56 a share), up 7 percent from profits of $7.9 million ($1.46) for the same quarter last year. For the first nine months of the year, United Virginia said profits were $24.8 million ($4.59), up 14 percent from profits of $21.6 million ($4.02) for the same nine months last year.

United Virginia's assets rose to $3.41 billion as of Sept. 30, up 6 percent from $3.21 billion at the end of the 1979 fiscal year.

Natinal Savings & Trust Co. yesterday reported a 28 percent jump in third-quarter profits to $1.3 million ($2.92 a share) from $1 million ($2.27) for the third quarter last year.

For the first nine months of 1980, profits rose from $3 million (6.59) at the close of the third quarter last year to $3.5 million ($7.66).