Giant Food Inc. reported yesterday a modest decline in profitability during the 12 weeks ended May 20, an indication that soaring food prices are having an adverse impact on both sides of supermarket checkout counters.

In the wake of government statistics showing an increase of some 6 percent in area retail food prices since January, Giant said its earnings suffered because of an "inability to fully pass along" higher wholesale prices and increases operating expenses.

The Landover-based company's profits to $2.95 million (89 percents a share) from $3.1 million (95 percents) in the same period last year, declined despite a 15.5 percent increase in quarterly revenues to $237 million, part of which represents inflation in retail food prices.

All of the figures relate only to continuing businesses of Giant Food, which closed its four big department stores earlier this year. When losses from the discontinued stores are included in results for the 12-week period last year, earnings per share for that period equal 85 cents a share.

On a $30 sale at Giant in the recent quarter, profits to the company were 37 cents compared with 45 cents in the same period last year. In recent weeks, retail prices have been boosted on many products at Giant and other food chains - reflecting the pressure on company profits caused by wholesale increases.

Area supermarket prices jumped 2.3 percent in April after a modest rise in March. Primary factors in the recent increase have been higher wholesale prices for beef and produce.

At the close of the recent quarter, Giant operated 115 stores including 41 food-drug combination units, 26 Pants Corrals that feature Levi's products: 3 garden centers, 8 optical shops and a gas station.

Giant recently opened a large food-drug unit in Reston and closed a food store in Richmond. Currently unders construction are two food-drug units and two Pants Corrals.

A company statement noted that Giant is "in strong financial consition," with cash and short-term investments of $43 million.

Giant also said it has differed until February 1979 the capitalization of certain leases on its account books. The leases were those signed before Jan. 1, 1977; has the leases been capitalized at this time, earnings per share would have been reduced an estimated 2 cents for both 12-week reporting periods.