American Express Co. reported yesterday that its profits rose by 32 percent in the third quarter of 1985 to a record $245 million.

Among other companies posting results yesterday:

* BankAmerica Corp., the nation's second-largest banking company, said its third-quarter profit fell 28.6 percent despite a pretax gain of $310 million on the sale of its world headquarters property. Burroughs Corp., the computer concern, reported net income of $32.2 million, or 71 cents a share, for the third quarter, down nearly 36 percent from $50.2 million, or $1.11 a share, a year earlier. Meanwhile, Apple Computer Inc. announced sales of $1.9 billion and earnings of $61.2 million for the fiscal year ended Sept. 27. This compared with sales of $1.5 billion and earnings of $64.1 million the previous fiscal year. Another computer concern, Coleco Industries Inc., shaking off its Adam computer losses and anticipating record sales on Cabbage Patch Kids and Rambo toys, reported record sales and earnings for the first nine months of 1985.

* The Coca-Cola Co. reported a per-share earnings increase of 10.4 percent to $1.48 in the third quarter and noted strong growth in its domestic sugar cola sector and in international operations. Net income for the quarter rose 11.6 percent to $196 million. For the first nine months of 1985, earnings per share rose 8 percent to $4.06, and net income increased 6.9 percent to $533 million. R.J. Reynolds said its third-quarter profits rose 12 percent from a year ago to $257 million, partly because of the contribution from recently acquired Nabisco Brands. The tobacco firm said inclusion of Nabisco's results from July 2 was the principal reason for a 47.8 percent rise in sales to $4.76 billion from $3.22 billion in the 1984 quarter.

* In communications, The New York Times Co. reported third-quarter earnings of $22.6 million, or 56 cents a share, a gain of 11 percent over $20.4 million, or 51 cents a share, in the 1984 third quarter. For the first nine months, net income rose 19 percent to $86.1 million, or $2.15 a share, from $72.6 million, or $1.83 a share, in the same period last year. American Broadcasting Cos Inc., faced with weak advertiser demand in its television and publishing operations and disappointing prime time ratings, reported its third-quarter earnings declined 38 percent from last year's record quarter that was bolstered by the Summer Olympic Games. RCA Corp. reported improved sales and earnings for the third quarter and the first nine months of the year. Earnings for the quarter rose 20 percent to $93.9 million, or $1.10 per share, from $78 million, or 74 cents per share, a year earlier. Sales were up 4.5 percent to $2.2 billion from $2.1 billion.

American Express, which earned $185 million in the 1984 period, said credit card use jumped 19 percent in the latest quarter to a total $14.1 billion worth of items charged.

Total revenues rose to $3.81 billion from $3.35 billion.

For the first nine months of 1985, profits rose to $537 million from $440 million and revenues were up to $11.06 billion from $9.4 billion.

American Express said strong earnings from foreign exchange dealings were partly offset by an increase in loans that are no longer being repaid, primarily in Latin America.

Income from investment services rose 20 percent to $36 million in the first full quarter since American Express acquired Lehman Bros. Kuhn Loeb.

Profit from insurance sales swelled by 144 percent to $34 million in the third quarter.

Warner Amex Cable Communications, which is half-owned by American Express, recorded a profit in the quarter.

American Express is selling its interest in Warner Amex to Warner Communications for $450 million cash.