Giant Food Inc. yesterday reported profits from continuing operations of $3.4 million ($1.01 a share) for the quarter ended Aug. 12, up 23 percent from the $2.7 million (82 cents) reported a year ago.

Net income from all operations showed an even greater increase, reflecting the heavy losses Grant suffered in its last fiscal year when it discontinued operations at four major department stores and a group of carpet centers.

Net income increased 56 percent over the 1977 quarter when Giant had a loss of $577,000 (17 cents) from the discontinued operations.

A spokesman for Giant, one of the Washington area's two major supermarket chains, said the increase in earnings from continuing operations reflected increased sales volume and a reduction in the company's effective tax rate due to the application of investment tax credits.Sales for the quarter increased 15 percent to $237 million from $206 million a year ago.

For the six months ended Aug. 12, net income increased 28 percent over a year ago, while income from continuing operations increased 8 percent. Income from continuing operations in the six months was $6.3 million ($1.90) compared with $5.8 million ($1.77) a year ago when Giant recorded a loss of $909,000 (27 cents) on its discontinued operations. Six-month sales increased 15 percent to $474 million from $411 million.

During its fiscal year ended Feb. 25, 1978, Giant reported a loss of $3.8 million from the operations it discontinued in February 1978 at the department and carpet stores. Giant now operates 115 stores, including 41 food-drug stores. 27 Pants Corral stores, 3 garden centers, 8 optical shops and one gas station. HAZLETON LABORATORIES CORP. reported a 28 percent increase in its earnings for the fiscal year ended June 30 to $1.3 million (72 cents a share) from $1 million (64 cents) for the preceding year. Revenues increased to $30 million from $24 million.

Fourth-quarter profits increased 18 percent to $51,000 from $318,000 a year ago as revenues increased to $8 million from $6 million. WASHINGTON GAS LIGHT CO. reported net operating income of $15.5 million for the 12 months ended July 31 compared with $17.8 million a year ago, as revenues increased to $353 million from $307 million.