Operating profits of Giant Food Inc. Jumped by more than 25 percent to $16.9 million last year and the supermarket chain's sales passed the billion dollar mark for the first time.

Giant's sales for the year ended Feb. 23 were $1.08 billion, up 15.5 percent from the $936.4 miilion of the prior year. Net income from continuing operations of $16.9 million ($5.09 per share) compared with earnings of $13.4 million ($4.08).

A Giant official said the main reason profits grew faster than sales was that "existing stores enjoyed substantial volume increases."

The decision to keep most of the company's supermarkets open 24 hours a day "accounted for a portion of the extra volume", the company source said.

Giant officials noted that the 15 percent sales gain was "substantially above that which could be attributed to inflation."

Giant opened three new food and drug store combinations during the fiscal year, remodeled four older stores, and added three units to its Pants Corral jenas shop chain during the year.

The supermarket chain also indicate productivity and profitability were improved by the company's accelerated program of converting to computer checkouts.

Giant added computers to 33 stores last year, and now has 87 computer checkout sotres. By Aug. 20 all Giant stores will have computer checkouts and the chain will be the first in the nation to be completely computerized.

Giant's sales and profit figures were all restated because of new accounting rules requiring capitalization of leases. Operating results are for continued oerations; the company's operating income last year was reduced by a $3.3 million charge for closing of Giant Department Stores, which lowered fiscal 1978 net income to $9.9 million ($3.05).

For the final quarter of fisccal 1979, Giant sales increased to $360.4 million from $311.7 million.

Operating income for the quarter was $7.9 million, compared with operating profits of $5 million ($1.54) and net income after a $2.3 million loss from store closings of $2.76 million (83 cents).

In New York, the Great Alantic & Pacific Tea Co. reported its supermarkets lost $52.2 million in the year ended Feb. 24, most of it because of A&P's latest "restructuring."

The troubled supermarket chain said $51.67 million of its loss was due to the closing of 174 stores and several warehouses and procesing facilities. After writing off that cost, A&P's operating loss for the year was about $530,000 - roughly equivalent to its $569,000 profit (2 cents) the previous year.

Despite the store closings, A&P sales increased to $7.47 billion from $7.29 billion.

For the fourth quarter of fiscal 1979, A&P lost $36.9 million, most of that also due to restructuring, the company said. Sales for the quarter-were $1.9 billion, up from $1.87 billion a year earlier.

In the final quarter of 1978 A&P showed a profit of $895,000 (4 cents).

A&P's fourth quarter loss this year was the second largest ever for the chain, which reported a $179 million deficit for the final quarter of 1974 when it first began retrenching and closing stores.

Further closings and reorganizings have failed to stem the losses and A&P announced a few weeks ago that a group of major shareholders had agreed to sell 42 percent of the company to the German Tengelmann Group for $75 million. CAPTION: Illustration, no caption, The Washington Post