Giant Food Inc. yesterday reported that sales and earnings in this year's third quarter were substantially higher than the comparable 12-week period in 1981.

In another earnings report made public yesterday, Washington-based Woodward & Lothrop said its third-quarter profit represented a "modest" improvement.

Giant, which operates a 130-store supermarket chain from its Landover headquarters, said net income for the quarter increased 13 percent to $7.6 million ($1.57 a share) on sales totaling $422.6 million, from $6.8 million ($1.38) and sales of $398.4 million in 1981's third quarter.

Net income as a percent of sales rose from 1.70 percent to 1.81 percent.

Pre-tax income was $13.7 million, or 3.24 percent of sales, compared with $10.7 million, or 2.69 percent, in last year's third quarter.

Giant also reported growth in sales and earnings for the 36-week period ended Nov. 6. The company said net income at the end of three quarters was $24.1 million ($4.91), compared with $4.5 million (92 cents). Sales were up 10 percent, from $1.1 million to $1.25 million.

Giant returned to profitability during the 12-week period that ended Nov. 7, 1981, after experiencing a loss in the previous 24 weeks. Current 36-week earnings of 1.93 percent as a percent of sales were nearly at levels reached in the prior four quarters, Giant officials said.

Woodies said net income for the third quarter ended Oct. 30 increased 3.5 percent, from $1.8 million (75 cents) in 1981 to $1.9 million (78 cents). Sales totaled $87.2 million, compared with $82.3 million a year ago, for an increase of 6 percent.

For the first nine months of this year, Woodies recorded net earnings of $3.2 million ($1.28), a 23 percent decline compared with income of $4.1 million ($1.67) in the comparable period last year.