SEOUL—At 7 p.m. on Fridays, Seoul City Hall’s electricity is cut and the 12-story building goes dark. It is the only fail-proof way to make sure municipal employees leave the office on time.

A new law caps South Korea’s workweek at 52 hours, including overtime—a 16-hour cutback—and calls for fines and up to two years in prison for employers that violate the rule.

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