The nation's biggest bank reported a 13.7 percent drop in third-quarter profits, while the second-largest posted a 52 percent gain.

BankAmerica Corp., holding company for Bank of America, said its net income fell to $103 million (70 cents a share) from $119.3 million (81 cents) last year.

Samuel H. Armacost, BankAmerica's president and chief executive, attributed the decline to "generally difficult economic conditions both in the United States and abroad" that forced the company to increase its provision for loan losses.

Nine-month profits fell 5.7 percent to $340 million ($2.30) from $360.7 million ($2.45) a year earlier.

Citicorp, parent of Citibank, the nation's second-largest commercial bank, reported a net profit increase of 52 percent for the third quarter to $199 million ($1.54 a share) from $131 million ($1.04) a year ago.

Nine-month net income rose 63 percent to $530 million ($4.11) from $326 million ($2.59).

The holding company said earnings reflected new pricing policies, repositioning of assets, investments in technology and stringent credit policies.

Philip Morris Inc., a major retailer of tobacco and beverage products, said yesterday that its third-quarter earnings rose 20.2 percent to $250 million ($1.99 a share) from $207.9 million ($1.66) a year ago.

Revenue was $3.1 billion, up 7.5 percent from $2.9 billion.

Nine-month earnings rose 21.8 percent to $606.1 million ($4.84) from $498.5 million ($3.99), and revenue climbed 8 percent to $9 billion from $8.3 billion.

Republic Steel Corp. lost $75.5 million in the third quarter, bringing the company's nine-month loss to $178.5 million.

Republic, which has denied repeated rumors that it is filing for bankruptcy, attributed the loss to the depressed steel industry.

Nine-month net income was $168.3 million ($10.41 a share) in 1981. Revenues in the third quarter amounted to $601.5 million compared with $1.1 billion in 1981; nine-month revenues fell to $2.2 billion from $3.4 billion.