Half- and quarter-hour differences are usually because of local authorities that didn't fully support the change to Greenwich Mean Time (GMT) in the 1880s.
India, which lies between two time lines, adopted the 30-minute mark to keep sunrise and sunset from occurring too early or too late on the edges of the country.
The time in Greenwich, England, was used beginning in the 15th century to aid ocean navigation. The International Meridian Conference in 1884 extended this, creating an International Date Line and 24 time zones for each hour.
Before this, cities kept their own clocks—the U.S. had more than 300 different local times before GMT took effect on Nov. 18, 1883. Telegraph lines were used to synchronize the country.