The nation's 36 largest freight railroads showed significant increases in operating earnings and revenues in the third quarter of 1981 and for the 12 months ended Sept. 30, 1981, according to a recent Interstate Commerce Commission report.

The ICC said net railway operating income for the railroads reached $429.7 million in the third quarter of last year, a 76 percent increase over the corresponding period of 1980. The group of railroads includes those with annual operating revenues of $50 million or more.

Operating revenues in the July-September period for the group of railroads rose 14 percent to almost $8 billion from almost $7 billion in the same period of 1980.

The ICC reported that for the 12 months ended Sept. 30, 1981, net railway operating income rose 55.3 percent over the prior 12-month period to $1.7 billion.

Operating revenues for the 12 months totaled $30.7 billion, an 11.5 percent increase. The ICC said the increase in revenues was due primarily to higher rates; there was only a slight increase in freight volume for the 12-month period.

The ICC noted that Consolidated Rail Corp., the federally subsidized freight railroad included in its listing, showed a significant improvement last year. In the 12 months ended Sept. 30, Conrail cut its net operating loss by $325.7 million to $101.8 million, its net loss by $365.2 million to $147.6 million. Its net operating loss was reduced to $21.3 million in the third quarter from a loss of $136 million in the same period of 1980.

The rate of return on net investment for the rails increased to 5.13 percent for the 12 months ending in September from 3.59 percent for the corresponding prior period.