Domestic automakers sold 15.8 percent more new cars in the last 10 days of August than in the same period last year--191,170 compared with 165,072.

That increased the seasonally adjusted annual rate--the total amount of new cars that would be sold by the end of the year if sales continue at their current pace--by 16 percent to 6.5 million, from a rate of 5.6 million in the last 10 days of August 1982.

The increase in U.S. new-car sales at the end of August marked the 11th consecutive sales gain this year. However, the gain was less than those recorded in June and July and for the first two reporting periods in August. Ironically, the slowdown was caused partly by the fast sales pace of early summer, which depleted domestic new-car inventories.

For example, Automotive News, an industry trade journal, recently reported that dealer new-car shortages "ranged from low inventory across one or two lines to severe shortages across their entire lineup.

"Big cars, luxury cars, performance cars and vans were cited most often as being in short supply. Many dealers say they are losing sales because of low inventories or long waiting periods," the trade journal said.

American Motors Corp., the nation's fourth-largest automaker, reported the largest sales gain for the end of August. The company, still riding the popularity of its Alliance line, sold 5,633 cars during the period, a 148 percent increase over 2,263 cars sold in the year-ago period. AMC is depending on a new hatchback version of the Alliance and on a new down-sized Jeep to keep up its sales vigor in the 1984 model year, which begins this month.

Chrysler Corp., No. 3, sold 22,161 new cars, an 18.9 percent increase over 18,637 sold in the end of August 1982. Ford Motor Co., No. 2, sold 45,513 new cars during the period, an 18 1/2 percent increase over last year. General Motors Corp., No. 1, sold 112,095 new cars, a 10 percent increase over 101,867 sold in the 1982 period.

Volkswagen of America, despite an expensive advertising campaign this summer, remained stuck on the slow-sales trail, selling 3,891 new cars during the period, 0.3 percent more than 3,881 sold in the comparable 10 days of 1982.

American Honda Manufacturing Co., which only began building cars (Honda Accords) in the United States this year, sold 1,877 cars at the end of August.