ARA Services Inc. of Philadelphia has agreed to acquire Smith's Transfer of Staunton, Va., in an exchange of stock worth $84 million, the two companies announced yesterday.

Smith's is the biggest truck line in Virginia and the eighth largest in the nation with sales last year of $250 million.

A conglomerate whose sales will top $2 billion this year, ARA runs a $1-billion-a-year food service business, is a major distributor of magazines and books in Washington and 21 other cities, and runs nursing homes, uniform rental services, and school buses.

Under the agreement in principal approved by board of directors of both companies yesterday, each share of Smith's stock will be traded for nine-10ths of a share of ARA.

Before trading was suspended yesterday, by the New York Stock Exchange Smith's stock was trading for $29.50 a share, its all-time high.

ARA stock closed yesterday at $38 1/8. At that price nine-10ths of a share would be worth about $34, and the 2.5 million shares of Smith's stock outstanding would be valued at $84 million.

The largest stockholder of Smith's is its chairman, R. R. (Jake) Smith, 65, whose brothers founded the company by hauling cattle to market for Shenandoah Valley Farmers. Smith owns 8.7 percent of the company's stock worth about $7.5 million in ARA's stock.

The joint announcement said Smith and the truck line's present management team would continue to manage the company after it is acquired by ARA.

The merger requires the approval of shareholders of both companies and several regulatory agencies, including the Interstate Commerce Commission.

In addition to the proposed exchange of stock, ARA said it may buy up to 250,000 shares of Smith's -- 10 percent of the stock -- on the open market for cash.

ARA officials said that company had been seeking to expand its service-oriented operations into the trucking field and looked at several other truck lines before approaching Smith's.

Last Friday, Smith's revealed it had received a takeover proposal and, long meetings yesterday, the preliminary agreement with ARA was announced. The two companies still must agree to terms of a definitive agreement; that could take three to six months, a spokesman said.

Smith's carved its niche in the highly competitive trucking business by specializing in less-than-truckload shipments, small but profitable business that many truck lines ignored.

Founded 20 years ago as a food service company, ARA generated 55 percent of its revenues from that business last year, said David Dayton, vice president for customer relations. ARA's sales for 1978 totaled $1.75 billion and the company earned $252 million in profits. Revenues will top $2 billion for the fiscal year that ends this month, Dayton said.

ARA provides food services at ball parks, airports, factories, office buildings and hospitals. Its second largest revenue producer -- about 17 percent of 1978 sales -- is book and magazine distribution. Another 15 percent comes from a health care division that operates nursing homes and hospital services.