Explanation: To understand the time difference between IST and Shillong, we need to consider the Earth's rotation and the longitudinal position of these locations. The Earth rotates 360 degrees in 24 hours, which means it rotates 15 degrees per hour (360 degrees / 24 hours = 15 degrees per hour). This rotation is the basis for time zones, which are typically defined by 15-degree segments of longitude.
India Standard Time (IST) is based on the 82.5°E longitude, which passes through the city of Allahabad. Shillong, the capital of Meghalaya, is located at approximately 92°E longitude. The time difference between two longitudes can be calculated using the formula:
\[ \text{Time difference} = \left( \frac{\text{Longitude difference}}{15} \right) \text{hours} \]
The longitude difference between IST (82.5°E) and Shillong (92°E) is:
\[ 92°E - 82.5°E = 9.5° \]
Using the formula, the time difference is:
\[ \text{Time difference} = \left( \frac{9.5°}{15} \right) \text{hours} = 0.633 \text{hours} \]
Converting 0.633 hours to minutes:
\[ 0.633 \text{hours} \times 60 \text{minutes/hour} = 37.98 \text{minutes} \approx 38 \text{minutes} \]
Therefore, the local time at Shillong would be 38 minutes ahead of IST. If it is 10 am IST, the local time at Shillong would be:
\[ 10:00 \text{am} + 38 \text{minutes} = 10:38 \text{am} \]
This calculation shows that the correct answer is 10:38 am. The key concepts to remember are the relationship between longitude and time zones, the formula for calculating time difference, and the direction of time difference (whether to add or subtract based on the longitudinal position).