The reason some time zones are 30 minutes off instead of a whole hour has to do with historical, geographical, and practical considerations. Time zones were established to make it easier to coordinate activities and scheduling across vast geographic areas. However, the implementation of time zones doesn’t always align perfectly with political or geographical boundaries. Here are a few reasons why you might find 30-minute time zones:

1. Geographical oddities: Some areas are geographically located approximately halfway between two time zones. Instead of creating a new, unique time zone, it was sometimes decided to split the difference and use a 30-minute offset. An example of this is the Navajo Nation in the United States, which spans multiple states and is split between Mountain Time (MT) and Pacific Time (PT). Parts of the Navajo Nation are in Mountain Time, and other parts are 30 minutes ahead in Pacific Time.
2. Territorial autonomy: In some cases, a territory or region might have had the autonomy to choose a time zone that was 30 minutes different from its neighbors for historical reasons. For example, in India, the state of Kerala used to observe its own time zone, which was 30 minutes ahead of the rest of the country. This was later standardized to align with the Indian Standard Time.
3. Administrative convenience: Sometimes, a 30-minute offset can be a practical decision to keep a region within the same time zone as a major city or administrative center, even if the geography suggests a different offset. This can be for the sake of convenience in conducting business and communication.
4. Energy efficiency: In the past, when daylight saving time was not observed in some areas, a 30-minute offset could help maximize the use of natural light. For example, in the Soviet Union, some areas had 30-minute time zones to extend daylight hours during the winter.
5. Agricultural practices: Before the widespread use of electricity and modern transportation, agriculture played a significant role in determining local time. Some areas might have adopted a 30-minute offset to align with sunrise and sunset times that were not evenly divisible by an hour.
6. Political decisions: Political considerations can also play a role in establishing a 30-minute time zone. For example, in some countries with federal systems, states or provinces might have the authority to decide on their time zone, leading to some areas being 30 minutes off.

Examples of countries with half-hour time zone offsets include Nepal (UTC+05:45), India (UTC+05:30), Myanmar (UTC+06:30), Nauru (UTC+12:00), and parts of Australia (Central Western Time, UTC+08:45).

Overall, the reasons for 30-minute time zones are often a combination of historical accident, practical considerations, and local autonomy. As global standards for time keeping have become more uniform, some of these unique time zones have been abolished or changed to align with the nearest whole-hour time zone for consistency and ease of communication.