Giant Food Inc. posted a 17 percent increase in profits and a sales gain of 8 percent in unaudited results for the first quarter, the company announced yesterday.

The Landover-based supermarket chain said net income for the 12-week period ending May 21 was $8.8 million (60 cents a share) compared with $7.5 million (51 cents) in the first quarter of 1982. Sales increased from $411.9 million a year ago to $444.8 million.

Sales were up 8 percent even though the inflation rate for food remained at relatively low levels, the company noted.

Net income as a percent of sales rose from 1.8 percent to 2 percent, well above the industry average, which is just above 1 percent. This was the sixth consecutive quarter in which Giant's earnings were roughly the equivalent of two cents on each sales dollar.

Giant operates 131 supermarkets, 70 of which are food-pharmacy combinations. The company operated 132 supermarkets a year ago but sold three stores in the Richmond area last June. Excluding the sales of those stores from 1982, results would have given Giant a sales increase of 9 percent for the 12-week period, the company said.