Financial General Bankshares Inc. reported yesterday its second-quarter profits dropped to $3.31 million (48 cents a share) from $4.09 million (59 cents) last year.

The bank holding company also showed a $39,000 loss on securities transactions during the quarter, reducing net income to $3.27 million (47 cents.)

Rapid declines in interest rates were blamed for the drop in second-quarter profits of the Financial General banks, the third-largest financial institution in the Washington area.

For the first six months of the year, Financial General's earnings were ahead of the 1979 figures. The company reported operating earnings of $7.85 million ($1.13), up from $7.78 million ($1.05) last year. After securities transactions, the banks earned $7.78 ($1.12) compared with $7.22 million ($1.04).

In other reports, Allegheny Beverage Corp. reported a 15 percent increase in second-quarter profits compared with the same period in 1979. The Baltimore-based Pepsi Cola bottler, which is trying to buy control of Washington's Macke Corp., reported second-quarter profits of $1.82 million (47 cents a share), up from $1.58 million (41 cents) for the second quarter last year.

For the first half of 1980, Allegheny Beverage's profits rose to $2.66 million (69 cents), up 29 percent from $2.06 million (54 cents) for the first half of 1979.

But the company's sales dropped slightly in the second quarter, falling from $37.53 million in 1979 to $36.97 million for the 1980 second quarter. First-half sales are also down slightly, decreasing to $65.41 million for the first half of this year from $65.89 mllion for the same period last year.

The company blamed the sales decline to the effects of the recession on consumer demand. The company also said its $12.93 million investment in common stock of the Macke Co., a holding representing about a third of Macke's stock, will not show up on Alleghany Beverage books until the 1980 fourth quarter.

Metropolitan Federal Savings and Loan Association of Bethesda and its wholly owned subsidiary, MFS Service Corp. reported earnings for the second quarter of $93,068 (20 cents a share), down 83.1 percent from $551,539 ($1.17). Revenues were $5.99 million, up 4.9 percent from $5.71 million. Earnings for the first half were $537,405 ($1.14), down 50.7 percent from $1.1 million ($2.31). Revenues were $11.9 million, up 6 percent from $11.2 million.

Scope Inc. of Reston reported earnings for the second quarter of $583,000 (48 cents a share), down from $859,000 (70 cents) a year earlier. Sales were $18.1 million, up 5 percent from $17.3 million. First-half earnings were $1.1 million (93 cents), down 36 percent from $1.8 million ($1.45). Revenues were $35.3 million, a 7 percent increase from $32.8 million.