The Washington Post Co. reported a 13.6 percent increase in second-quarter profit.

The company announced net income of $51.8 million, or $6.84 a share, up from $45.6 million, or $5.74 a share, a year earlier. Revenue for the quarter totaled $1.0 billion, down 5 percent from $1.06 billion for the second quarter of 2011.

Net income from continuing operations fell 28.6 percent after taking into account the sale of two parts of the company’s Kaplan subsidiary.

The company’s cable television division turned in a solid profit, and broadcast television earnings soared 34 percent, buoyed in part by a surge in political advertising in this election year. But the Kaplan education and newspaper divisions were still ailing. Broadcast television was the only Post division reporting higher operating profit than a year ago.

Operating income plunged 84 percent at the once-high-flying Kaplan education subsidiary. Enrollment at Kaplan’s higher education unit, which last quarter showed signs of bottoming out after a year of retrenchment, once again fell. Student enrollment at the higher education unit dropped 11 percent from March 31 this year to 67,605, the lowest level since 2007. New student enrollments, which had been up slightly in the first quarter, were down 1 percent.

The company said: “Kaplan will likely incur additional restructuring costs in the second half of 2012.” With lower enrollment, Kaplan spent $5 million on severance and restructuring in the second quarter.

The Kaplan subsidiary’s one bright spot was its test-preparation operations, which earned $2.7 million compared with an $11.6 million operating loss during the second quarter of 2011.

Overall Kaplan revenue in the second quarter totaled $558.4 million, down 9 percent but still accounting for 55 percent of the entire company’s revenue. Kaplan sold two units, Kaplan Learning Technologies and EduNeering.

The flagship Washington Post newspaper was battered by a 15 percent drop in print advertising from the year before. The paper’s circulation also continued its steep slide. The company did not release quarterly figures, but the average daily circulation of the newspaper during the first six months of 2012 fell 9.3 percent from the same period of 2011. Sunday circulation was down 6.1 percent in the same period.

Online ad revenues rose 8 percent at the news division in the second quarter compared with the same period last year, reversing recent declines. But the $2 million increase in online revenues covered only a small part of the $9.9 million decline in print ads.

Overall the newspaper division, which includes Slate and, reported an operating loss of $15.9 million in the second quarter, compared with a $2.9 million loss for the same period in 2011. The second-quarter 2012 results included a $3.4 million expense for severance packages for news staff and other accounting charges. The division’s second-quarter revenues were $151.8 million, down 7 percent from the year before.

The company also announced this week that it had divested itself of its ownership of Avenue 100 Media. Over the past four years, The Post Co. has written off $109 million in connection with its acquisition of Avenue 100 Media, formerly known as Course Advisor. The struggling firm, which is now owned by its management, is a digital marketing company that sources leads for academic institutions and recruiting organizations.

The Post Co. continued to rely on its television operations. Cable television revenue increased slightly and operating income fell 5 percent to $38.4 million in the second quarter. An increase in customers buying high-speed data services and telephony subscribers was offset by a decrease in basic video subscribers.

Broadcast television’s operating income for the second quarter jumped 34 percent to $43.7 million and revenues rose 13 percent to $95.6 million. Political advertising helped but made up only part of the increase.

The Post Co. also said that it had repurchased 218,282 of its own shares at a cost of $74.5 million during the first six months of the year, virtually all of it in the second quarter. That averages to $341 a share. The company’s shares closed Thursday at $330.75 a share, down 1.7 percent.