Virginia National Bankshares reported a 37.5 percent increase in first-quarter operating profits yesterday.

Earnings totaled $3.8 million (84 cents a share) compared with $2.8 million (61 cents) during the same period last year. Since there were significant gains or losses from selling securities, net income was the same as operating income for both quarters.

W. Wright Harrison, chairman of the Norfolk-based bank holding company, attributed the gain to higher interest income on loans. Loan volume rose to $1.3 billion on March 31 compared with $1.2 billion a year ago.

Statewide deposits of VNB institutions rose to $1.9 billion from $1.7 billion.

New Virginia Bancorp. of Springfield reported a 73 percent increase in first-quarter profits to $408,438 (35 cents a share) from $235,548 (20 cents) in the 1977 period.

Loan volume increased by 36 percent to $87 million and deposits increased 14 percent to $135 million.

Manor Care Inc., a nursing home firm in Silver Spring, reported profits in the nine months ended Feb. 28 were unchanged from a year earlier at $1.5 million (91 cents a share), although sales rose to $27 million from $22 million.

In the third quarter, Manor Care profits rose sharply to $1 million (62 cents) from $176,563 (10 cents) and revenues increased to $9.3 milion from $7.5 million.