MCI Communications Inc., the company that offers cut-rate long distance telephone service in competition with the Bell System, reported yesterday its profits more than tripled in the latest quarter.

MCI's earnings for the three months ended Sept. 30 jumped to $15.4 million (31 cents a share) from $4.1 million (5 cents) in the same period a year ago.

Revenues and earnings of MCI were aided by a 16 percent rate increase put into effect in July after American Telephone and Telegraph raised its long distance rates, the company said. Expansion of the service into several new cities and what MCI Chairman William G. McGowan called "continued strong growth in our customer base" boosted revenues for the quarter to $114.9 million from $52.7 million.

For the first six months of its current fiscal year the Washington communications company's revenues doubled -- from $100.8 million to $201 million -- and earnings jumped to $26.1 million (49 cents) from $6.8 million (10 cents). Earning per share increased more than total earnings because of changes in the number of shares outstanding.

USAir's profits for the three months ended Sept. 30 plunged to just over $7 million (40 cents) from $15.4 million ($1.19) while passenger and cargo revenues climbed to $268.1 million from $226.5 million.

So far this year, USAir's profits are running 8.6 percent behind the first nine months of 1980 at $38.4 million ($2.41) compared with $42.1 million ($3.28). Revenues have risen to $816 million from $704 million.

"The air traffic controllers' strike in August and September absolutely ruined our hub at Pittsburgh," said Gerald J. King, vice president for public affairs. However, King attributed some of the decline to an additional 5 million outstanding shares.

Virginia National Bankshares of Norfolk posted record quarterly net earnings of $7.5 million ($1.06), up 67 percent from the $4.5 million (64 cents) of a year ago. Earnings before securities transactions for the quarter ended Sept. 30 were up 72 percent to $8.1 million from $4.7 million.

Nine-month net earnings of the $2.7 billion bank holding company increased 31 percent to $21.3 million ($2.98) from $16.3 million ($2.33) in the same period a year ago.

The $3.8 billion network of United Virginia Banks, however, reported its net for the latest quarter slipped slightly to $8.1 million ($1.46) from $8.4 million ($1.55) even though income before securities transactions climbed to $9.3 million from $8.4 million.

United Virginia's net earnings for the nine months ended Sept. 30 increased to $26.6 million ($4.88) from $22 million ($4.09) while income before securities transactions jumped to $28.4 million from $24.8 million