General Motors Corp. and Ford Motor Co. both reported increases in car sales for the final 10 days of March to help boost U.S. sales 23 percent from 1981, but automakers said today that sales for the month dropped 23 percent, producing the worst selling rate since 1975.

In the final third of the month, U.S. automakers sold 236,937 cars compared with 192,638 a year ago. Sales for the month were 575,608 compared with 719,044 a year ago.

GM's 53 percent year-to-year increase in sales in the last 10 days of the month was prompted by the end of rebates, while its sales of 349,506 cars in March were down 23 percent from the same month last year.

Ford posted a modest 3.2 percent year-to-year sales increase in the final 10 days, and its sales for March were 135,210, down 17.8 percent.

Chrysler Corp. said it sold 7 percent fewer cars in the final 10 days of the month. Its sales of 72,627 autos for March were down 24 percent.

Volkswagen of America Inc. sold 32.8 percent fewer cars in the final 10 days. Its March sales of 9,987 were down 40 percent from 1981.

American Motors Corp.'s sales dropped 40 percent in the last 10 days and 39.7 percent over the month.

Imports totaling 194,208 took 25.2 percent of U.S. sales--marking the lowest daily selling rate for imports since March 1978. That compared with 222,158 sold in March 1981, or 23.6 percent of the market.

Combined industry sales for March were 769,816, down 21.3 percent from 941,525 sold in March 1981.