The sun rises two hours earlier in Arunachal Pradesh as compared to Gujarat in the west but the watches show the same time. How does it happen?
India has a longitudinal extent of 30°. Due to this there is a time lag of two hours between the sunrise on the easternmost and the westernmost horizons of India. Due to rotation, the earth takes 4 minutes to rotate through 1° of longitude. The difference in time is one hour for 15° of longitude. Therefore, for a longitudinal extent of 30° of India, there is a time lag of 2 hours.
When it is 6 a.m. in Arunachal Pradesh, it is still 4. a.m. in Gujarat. But the watches in all parts of India are run according to standard time measured from 821/2°E longitude.
So, the watches in Arunachal Pradesh and Gujarat show the same time despite the different sunrise.