Xerox Corp. yesterday reported a 7 1/2 percent increase in second-quarter profits and said the number of installed Xerox copiers and duplicators rose faster than in any second quarter in the company's history.

Xerox said it earned $183.8 million ($2.18 a share), up from $170.9 million ($2.02) in the same period a year earlier. Revenues rose 10.1 percent to $2.24 billion from $2.04 billion.

In the first six months. Xerox said it earned $341.2 million ($4.04), up from $317.3 million ($3.76). Revenues were up to $4.29 billion from $3.89 billion.

"Our first-half growth in revenue, net income and earnings per share was adversely impacted by the strengthening dollar," Chairman C. Peter McCulough and President David T. Kearns said in a statement.

Consolidated Rail Corp. yesterday reported a net income of $13.8 million for the three months ended June 30 -- only the second quarterly profit in the government-chartered railroad's five-year existence.

The second-quarter income was a turnaround from the same period last year when Conrail lost $48.3 million.

Consolidated revenue for the 1981 quarter was $1.075 billion, compared with $993.8 million for the second quarter of 1980.

For the first six months of 1981, Conrail reported a loss of $52.1 million, compared with a loss of $143.7 million in the first half of 1980. Consolidated revenue in the half was $2.137 billion, versus $2.009 billion in the 1980 period.

Conrail attributed the second-quarter profit to "continuing efforts to reduce costs in the face of declining traffic."

The corporation said the United Mine Workers' coal strike contributed heavily to a 10.4 percent drop in carloadings from the second quarter of 1980. The corporation said, however, the 49.3 percent drop in coal loadings was offset partially by gains in shipments of coke, primary metals, automobiles and auto parts.

Conrail's announcement was not a surprise. It said two weeks ago it expected it would be able to announce a second-quarter profit of approximately $13 million.

Conrail registered its only other profit -- a net income of $23 million -- in the second quarter of 1979.