Sharply higher first quarter profits were reported yesterday by two of Washington's biggest retailers, Giant Food Inc. and Garfinckel, Brooks Brothers, Miller & Rhoads, Inc.

Giant attributed its 46 percent increase in earnings to a 13 percent boost in sales and to increased efficiency due in large part to installation of more computer checkouts.

A 12 percent sales improvement gave Garfinckel Corop. a 20 percent increase in operating profits and a nearly $1 million gain from sale of the Joseph R. Harris division doubled the company's net for the quarter.

For the 13 weeks ended May 5, the Garfinckel retail stores earned $2,354,000 (52 cents per share) compared with $1,157,000 (25 cents) in the comparable period a year earlier.

Sales were $86.6 million, up from $77.3 million.

Excluding the Harris losses, Garfinckels reported after-tax operating income of $1.64 million (36 cents) this year compared with $1.3. million (30 cents) last year. The Harris stores lost $280,000 in this year's first quarter and $232,000 a year ago.

The stores were sold during the quarter to Petrie Stores Copr, for about $4 million, producing a $999,000 non-recurring profit.

Garfinckel Corp. purchased the Harris women's wear stores in 1971 from members of the Joseph R. Harris family for 560,000 shares of Garfinckel stock worth $8.4 million at that time. Last year the Harris family holdings sold 466,000 shares to Gamble-Skogmo Corp. for $13.5 million in cash and notes.

Garfinckel's earnings for the remainder of the year are expected to be aided by elimination of the losses from the Harris stores.

Giant Food reported its sales for the 12 weeks ended May 19 increased to $268 million from $237 million, producing net income of $4.33 million (87 cents) against $2.95 million (59 cents).

Giant said it's net amounted to 1.61 percent of sales, up from 1.25 percent of sales, but noted its gross margins were still within the guidelines of the Council on Wage and Price Stability.

"Any improvement in sales generally adds to bottom line performance," a Giant officer noted, "and when a sales gain is coupled with lower operating expenses, the impact, on the bottom line can be substantial."

Giant said its improved efficiency came in part by adding computer checkouts to 21 more stores during the quarter. The company now has 117 stores, two more than in the same period a year ago.

A study of local market sales released earlier this week estimated Giant had increased its share of the business and now controlled 33 percent of the market, compared with about 30 percent for second-ranked Safeway.

Capital Mortgage Investments reported earnings of $249,000 for the quarter ended March 31 compared with $817,000 in the same period a year ago.

The Chevy Chase real estate investment trust said this year's earnings included a $348,000 credit from settling a claim against a bonding company. A year earlier the company had a $270,000 operating loss, but made a profit because of a $1 million extraordinary gain.

Capital Mortgage also announced it has ended negotiations for a merger with Columbia Corp. and said it still is having problems paying its debts.

Interest due May 15 on 6.5 percent convertible debentures is being "withheld pending further negotiations with the trust's creditor banks," the company said. The banks have delayed a scheduled increase in the interest rate from 1 percent to 3 percent on $28 million in overdue loans.

Washington Gas Light Co. reported a $1.02-per-share decline in common stock earnings for the 12 months ended April 30, after eliminating the effect of accounting changes.

In February, Washington Gas began counting as revenue the cost of gas delivered to customers but not yet billed.

Under that system, Washington Gas showed common stock net income of $12.89 million ($2.96 a share), down from $12.90 million ($2.97) a year earlier. The accounting change added $1.01 a share to this year's revenues, the company explained.

Washington Gas said a delay by the District of Columbia Public Service Commission in acting on a rate increase application filed in July 1977 was the major reason for the lower earnings.

The utility's revenues for the latest 12 months were $354 million, up from $352 million a year earlier.

Baltimore Gas and Electric Co. also reported lower common stock earnings. For the four months ended April 30, the big Maryland utility earned $43.5 million ($1.40 a share), down from $44.5 million ($1.45).

For the latest 12-month period, Baltimore Gas reported common stock earnings of $103 million ($3.34), up from $96 million ($3.18).

The company said a two-tier electric rate system implemented in January will mean somewhat lower revenues in winter months and somewhat higher revenues in summer months. It reduced common stock earnings for both the four-month and 12-month periods by about 11 cents a share.

Tech Serv Inc. of Beltsvile reported an $8,586 loss for the nine months ended April 1 compared with a $155,000 deficit a year earlier. Revenues increased to just over $1 million from just under $900,000 the company said.

Tech Serv said sales of its life science and industrial products "continued to be weak," and the increase in sales was primarily due to a contract with the Army for radio-control systems for miniature target planes. CAPTION: Graph CONSUMER CREDIT; Because of errors in assembling the chart on consumer credit, some of the information in yesterday's chart was incorrect. The updated chart appears above.