Giant Food Inc., citing strong sales gains in new and older supermarkets in the 144-store chain, yesterday reported an increase in net income of slightly more than 13 percent for the second quarter and a sales increase of more than 10 percent.

Giant said net income was $15.3 million (51 cents a share) for the quarter that ended Aug. 15, compared with net of $13.5 million (45 cents) for the same period last year. Sales increased from $554.9 million in last year's second quarter to $613 million.

Net income as a percent of sales in this year's second quarter was 2.5 percent, down slightly from 2.55 percent in the first quarter, but up from 2.43 percent recorded by Giant in the second quarter a year ago. Measuring income as a percent of sales, then, means Giant earned 2 1/2 cents on every dollar in sales volume during the last quarter, which is well above the industry average.

For the 24-week period ending Aug. 15, Giant had net income of $30.8 million ($1.02) compared with $26.9 million (90 cents) for the comparable period a year earlier. Net income as a percent of sales increased from 2.44 percent to 2.52 percent. Sales for the period were up 10.52 percent, from $1.1 billion, to $1.2 billion