United Virginia Bankshares, the largest commercial banking company in the state, has reported a 17 per cent climb in profits during 1976. A batch of other area financial institutions also reported yesterday on last year's operations - generally showing significant gains in profitability.

UVB profits from operations, not counting gains or losses from selling securities, totaled $13.6 million ($2.55 a share) last year compared with $11.7 million ($2.19 in 1975. Net income was $13.8 million ($2.57 vs. $12.1 million ($2.27).

For the fourth quarter, UVB earned $3.6 million (66 cents) before securities transactions compared with $1.5 million (28 cents) in the final three months of the prior year.

Chairman Joseph A. Jennings said the 1976 gains were based on higher interest income, tighter control over expenses and lower reserves set aside to cover possible bad loans.

During 1976, UVB set aside $11 million for credit losses compared with $415 million the previous year. Loans in arrears totaled $50.7 million compared with $64.5 million at the end of 1975 and $58.4 million on last Sept. 30.

Total assets rose by $152 million during the year to more than $2.6 billion in Dec. 31, while daily average deposits last year were up 4 per cent to $1.9 billion.

Mercantile Bankshares Corp., a Baltimore-based bank holding company, reported 1976 profits before securities transactions of $8.96 million ($1.98 a share) compared with $8.15 million ($1.80) the previous year, an increase of 10 per cent. Deposits rose to $658 million from $600 million. The company's banks include Annapolis Banking & Trust, Bank of Southern Maryland, Citizens National of Laurel and Commerce Bank of Bethesda.

Central National Corp., a Richmond bank holding company, reported profits before securities transactions in 1976 of $4 million ($2.37) compared with $3.6 million ($2.15) the previous year, a gain of 12 per cent. Average daily deposits were up by 10 per cent during 1976 to $389 million.

Central National Bank of Maryland, based in Silver Spring reported operating profits of $239,000 in 1976 compared with $172,000 the previous year; no per-share figures were available. Deposits rose by 18 per cent to $35 million. Directors approved a cash dividend of 12 cents a share payable Feb. 4 to stockholders of record Dec. 31, as well as a 4 per cent stock dividend with a Jan. 5 record date.

Bank of Columbia of Washington reported a 51 per cent increase in profits during 1976 to $134,916 (31 cents) from $45,334 (16 cents) the previous year. Deposits rose by 43 per cent to $31 million, and loan volume grew by 48 per cent of $21 million.

New Virginia Bancorporation of Springfield, reported 1976 profits of $1.17 million ($1.04) compared with $850,563 (76 ccents) the previous year, a gain of 37 per cent. Average deposits in the recent year were up nearly 12 per cent of $109 million.

Bank of Maryland, based in Hillcrest of Height, reported 1976 profits of $471,502 ($2.67) vs. $390,597 ($2.19) the previous year, an increase of 21 per cent. Deposits increased by more than $7 million to $57.4 million.

Providence Savings and Loan of Vienna reported 1976 profits of $984,103 ($5.46) vs, $637,495 ($3.54) the previous year.

Second National Building & Loan of Ocean City earned $261,996 ($2.93) in 1976 vs. $99,303 ($1.14) the previous year. The S&L has offices in Easton, Salisbury and Ocean City.

Allied Capital Corp., a small business investment company based in Washington, reported a 13 per cent increase in profits for the six months ended Sept. 30. Net income was $300,400 (37 cents a share) compared with $265,800 (33 cents). Revenues rose 16 per cent to $792,700.

Directors of Allied declared a regular quarterly dividend of 12 cents a share, payable March 31 to stockholders of record March 1.

Computer Data System, Inc., a professional services firm, reported that profits in the six months ended Dec. 31 fell to $31,500 (20 cents) from $112,600 (27 cents) in the same period of 1975. Revenues rose to $3.1 million from $2.5 million and directors declared a dividend of 5 cents a share, payable Feb. 28 to stockholders of record Jan. 28.