Merrill Lynch & Co., owner of the nation's largest stock brokerage and investment business, yesterday completed its entry into the Washington real estate business by acquiring Colquit-Carruthers Inc., a medium-sized broker here that currently operates 26 District or suburban offices.

Financial details of the transaction were not disclosed. The parties, which have been discussing a takeover by Merrill Lynch for several months, said only that the New York company acquired "certain assets" of Colquitt-Carruthers. Industry sources said that could be translated into purchase of a large, controlling interest for more than $10 million.

Effective immediately, all Colquitt-Carruthers personnel have been transferred to Merrill Lyncy Realty/Chris Coile Inc., of Baltimore, and that also will be their firm's name. Control of the Annapolis and Baltimore real estate firm started by Chris Coile in the early 1970s was acquired by Merrill Lynch Realty earlier this year.

Coile, who stayed on as president of the Merrill Lynch subsidary in Baltimore, will continue in that post with the additional Washington area offices Merrill Lynch/Chris Coile will have 45 offices in the two metropolitan areas; some Colquitt-Carruthers offices were closed earlier this year, as the pinch of high interest rates cut the firm's sales by 20 percent.

The purchase of Colquitt-Caruthers is the 11th acquistition to date in Merrill Lynch's stated objective of establishing a nationwide real estate business.

The new Merrill Lynch/Chris Coile business in Washington includes commercial investment and property management divisions as well as a training center for sales associates.The combined Baltimore-Washington real estate firm will be one of the largest single realty business in the country.