International Bank of Washington and Equitable General Corp., a McLean insurance holding company, yesterday reported substantial increase in profitability for the first nine months of 1977. Equitable directors also boosted their firm's dividend rate.

At International Bank (IB), a diversified financial services business, nine-month earnings jumped 110 percent to $8.6 million ($1.21 a share) compared with the restated $4.1 million (57 cents) for the same period last year.Revenues increased 24 per cent to $14.3 million.

For the third quarter alone, however, profits fell 11 per cent to $2.4 million (33 cents) compared with $2.7 million (37 cents) a year ago. Revenues were down slightly to $3.8 million from $4 million.

IB chairman George Olmsted said yesterday that improved results in life insurance industrial, finance and leasing operations produced a better than average third quarter. However, he said, revenues and profits were below record levels of a year ago and in the early months of 1977, because of lower earnings from property and casualty insurance and provisions for possible loan losses.

Foreign insurance, shipping and corporate business contributed 31 cents a share to nine-month earnings, up from 7 cents a year ago. As for casualty and property insurance firms in which IB has investments, underwriting profits trends "continue to be favorable" despite the decline from the third quarter of 1976, when underwriting profits were exceptionally good, he added.

Financial Security Group, IB's property and casualty holding company, reported nine-month earnings of $4.1 million ($1.36 a share) compared with $2.8 million (94 cents) a year earlier.

International General Industries, a member of IB's industrial group, reported a 14 percent increase in profits from continuing operations to $5.1 million ($2.88) vs. $4.5 million ($2.51). Revenues also were up 14 percent at $64 million.

"Sales of packaging systems, acoustical materials and metal parts are strong, markets are expanding and the trend of improving quarterly gains is expected to continue into 1978," Olmsted said of overall industrial company investments by IB.

Equitable General Corp., parent company of Equitable Life Insurance Co., reported profits from operations in the first nine months of $7.8 million ($2,43 a share), up 17 percent from $6.7 million ($2.05) a year earlier. The figures do not include investment gains or losses.