George's Radio and Television, a 15-store Washington and Baltimore chain, was purchased yesterday by two New York retailers, Douglas and Lawrence Jemal.

The pioneer appliance business was sold for an undisclosed sum by the estate of the late George Wasserman, who founded the firm 54 years ago. Since Wasserman's death in 1975, his widow, Janice Goldsten, has been chief executive.

With 10 stores in the Washington area and five more in and around Baltimore, George's has been a $30-million-a-year operation, trade sources estimated.

Not long ago George's closed two units, which were primarily furniture stores, in Silver Spring and on Allentown Road in Prince George's County.

The stores were closed to concentrate on the appliance, radio, television and home entertainment business, said Edgar Legum, who has served as interim president of George's for the past year. Legum took over management of the chain after the death of its president Herbert Filderman.

The Jemal brothers were reported to be touring the stores yesterday and could not be reached for comment on the plans for the chain.

George's was one of Washington's first mass merchandizers of appliances and related products.

George's has three stores in the District of Columbia, four in the Virginia suburbs, three in Washington's Maryland suburbs and five in the Baltimore market.