Planning Research Corp. has reported an 11.6 percent drop in first-quarter fiscal-year profits. The District-based consulting firm reported quarterly profits of $1.46 million (22 cents a share), down from first-quarter profits last year of $1.66 million (24 cents).

Revenues for the quarter rose from $61.8 million for the first three months of the company's fiscal year.

In other reports, Williams Industries Inc. reported profits for the fiscal year ending July 31 of $667,081 (87 cents a share) compared with a loss of $95,560 for the previous fiscal year. Revenues rose to $7.56 million from $7.31 million last year.

Williams, a construction firm based in Merrifield, Va., also announced the purchase of 41.6 percent of the outstanding stock of Atlas Machine and Iron Works Inc. of Gainesville, Va.

Richmond, Fredericksburg and Potomac Railroad Co. reported a 13 percent drop in third-quarter profits to $2.75 million ($7.67 a share) from $3.17 million ($8.85) for the same quarter last year. For the first nine months of the year, the company reported profits of $11.2 million ($31.16), up from $9.4 million ($26.28) for the same period in 1979.