MEMPHIS, Tenn. (AP) _ Holiday Corp., a leading hotel and casino operator, on Thursday reported a 37 percent jump in third-quarter net income over a year ago but said its nine- month profit declined.

Net income for the three months ended Sept. 30 was $21 million, or 84 cents a share, compared with earnings of $15.4 million, or 63 cents, in 1987. Revenue declined to $422.1 million from $460 million.

For the first nine months Holiday's profit totaled $102.1 million, or $4.10 a share, on revenue of $1.22 billion. That was down from a profit of $126.7 million, or $5.21 a share, and $1.28 billion in revenue.

Holiday said its quarterly results reflected ''strong hotel and gaming operating results and an 18 percent reduction in interest expense.''

Holiday's subsidiaries include Holiday Inn, Embassy Suites, Hampton Inn, Homewood Suites and Harrah's.