United Virginia Bankshares Inc., the state's largest bank company, reported profits of $11.5 million ($1.96 a share) in the final three months of the year, a 25 percent increase over the $9.2 million ($1.59) it earned during the last quarter of 1981.

Meanwhile, Baltimore's Equitable Bancorp. said its fourth-quarter profits totaled $3.77 million ($1.02), up sharply from the $1.57 (36 cents) it earned in the final three months of 1981. Most of the increase was due to a $1.9 million reduction in the amount of money set aside for potential loan losses.

Both area banks reported increases in their 1982 earnings. Richmond-based United Virginia reported 1982 profits of $41.2 million, 15 percent more than the $35.8 million it earned in 1981. Equitable's 1982 earnings were $11.2 million, 13 percent more than the nearly $10 million it earned the year before.

United Virginia chairman Joseph A. Jennings said the 1982 earnings increased in large part because of a 17 percent widening in the spread between what the bank pays for deposits and what it earns on the loans it makes. That spread is called net interest income.

The bank said its income before securities losses was $44.4 million in 1982, 14 percent more than the $38.8 million of operating income it had in 1981.

United Virginia said its total non-performing assets (loans that are past-due or not being paid on the original schedule as well as real estate loans that have been foreclosed) were $45 million on Dec. 31, down from $51 million at the end of the third quarter, but above the $28 million the bank had on Dec. 31, 1981.

The bank set aside $18.8 million for possible loan losses in 1982, up from $11.1 million in 1981. The bank did not report the value of the loans it wrote off as uncollectible in 1982.

The bank company had assets of $4.8 billion at year-end, compared with $3.9 billion on Dec. 31, 1981. Loans rose to $3.3 billion, from $2.8 billion. Its deposits were $3.4 billion, compared with $2.8 billion at the end of 1981.

Equitable set aside $4.1 million for potential loan losses in the final three months of 1982, compared with a $6 million set-aside during the last three months of 1981. For the year the loan loss provision totaled $11.8 million, compared with almost $14 million in 1981.

Before losses on securities sales Equitable had income of $12.4 million last year, 27 percent more than the $9.8 million in operating income it reported in 1981.

Equitable had assets of $2.5 billion on Dec. 31, compared with $2.1 billion at the end of 1981. Its loans were $1.3 billion, almost unchanged from 1981, while deposits grew to $1.9 billion from $1.7 billion on Dec. 31, 1981.