Consolidated Rail Corp., the giant federally aided Northeast and Midwest railroad, reported a sharp increase yesterday in operating losses during the second quarter of 1978.

Conrail lost $60.9 million in the three months ended June 30, more than double its $27.6 million lost in the same period last year. Revenues for the nation's largest transporter of freight rose to $915 million from $867.5 million.

The recent losses brought Conrail's red-ink total for the first half of 1978 to $277 million compared with $235 million in the 1977 period, as revenues rose to $1.67 billion from $1.64 billion.

Conrail Chairman Edward Jordan said higher revenues reflected increased freight rates but that "inflationary increases" in labor and materials costs more than offset the higher volume.

"The financial results continue to reflect both the expenses required to address Conrail's substantial problems and also the continuing lack of adequate volume and revenue to cover its high fixed costs," Jordan said in a formal statement.

To catch up on maintenance deferred by owners of the six bankrupt railroad lines that merged into Conrail, the Philadelphia firm has stepped up work on tracks, freight cars and locomotives.

But Jordan said the additional investment required to upgrade facilities will create a larger loss this year than in 1977. For the first time in its 23-month history, Conrail is meeting its demand for locomotives that work, he added.

Greyhound Corp., owner of the nation's largest bus transportation firm, reported record profits for the second quarter of 1978 yesterday. Earnings totaled $19.7 million (45 cents a share) compared with $15.7 million (35 cents) a year earlier for a gain of 25 percent. Sales rose to $1.1 billion from $941 million.

In the first six months, Greyhound Profits were $27 million (62 cents), up 10 percent from $24.6 million (56 cents) last year. Revenues rose to $2.1 billion from $1.8 billion.

Chairman Gerald Trautman said substantial gains inthe company's financial operations were responsible for the quarterly increase. The firm owns the Armour food and consumer product businesses, and is engaged in food services, car rental and exhibit design.

Coca-Cola Co. reported record earnings yesterday for the second quarter and the first six months of 1978.

J. Paul Austin chairman of the Atlanta-based soft drink firm, told directors earnings rose 13 per cent in the second quarter to $109.75 million (89 cents a share) from $97.1 million (79 cents) in the same quarter a year ago.

Six-month net income was up 12.8 percent to $184.9 million ($1.50) from $163.9 million ($1.33) a year ago.

Sales also set a record, rising 21.3 percent in the quarter to $1.16 billion and 17.8 percent in the half of $2.07 billion.