Explanations:Understanding the concept of time zones and how they relate to longitude is crucial for solving this problem. Indian Standard Time (IST) is based on the longitude of 82.5°E, which passes through the city of Allahabad. This means that IST is the time at 82.5°E longitude. Shillong, the capital of Meghalaya, is located at approximately 92°E longitude. Since Shillong is east of the IST reference point, the local time at Shillong will be ahead of IST.
The Earth rotates 360 degrees in 24 hours, which means it rotates 15 degrees per hour. Each degree of longitude corresponds to 4 minutes of time difference (since 60 minutes / 15 degrees = 4 minutes per degree). To find the time difference between IST and Shillong, we need to calculate the difference in longitude between the two points and convert that difference into minutes.
The longitude of Shillong is 92°E, and the IST reference point is 82.5°E. The difference in longitude is:
92°E - 82.5°E = 9.5°
Since each degree of longitude corresponds to 4 minutes of time difference, the time difference between IST and Shillong is:
9.5° * 4 minutes/degree = 38 minutes
Therefore, if it is 10 am IST, the local time at Shillong would be 10:38 am. This is because Shillong is 38 minutes ahead of IST due to its eastern longitude.
It is important to note that the time difference is always calculated based on the direction of the reference point. In this case, since Shillong is east of the IST reference point, the time at Shillong is ahead of IST. If the location were west of the IST reference point, the time would be behind IST.
Understanding these principles helps in solving similar problems involving time zones and longitude differences. It is also useful in various competitive exams where such calculations are often tested.