why 82 degree 30'e has been selected as standard meridian of india
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It is close to the middle of the country (east-west). Also, it is a multiple of 7.5 degrees (half-hours) from the Greenwich meridian. Using 75 degrees E would be to far to the west, and using 90 degrees E would be too far to the west. Using 83.5 degrees E results in a nice 5.5 hour offset from London time.
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Note: The standard Meridian of India at 82′3 e at Mirzapur in Uttar Pradesh was taken as the standard Meridian because it splits the country into closely two equal parts The 82.50E longitude is smaller than 1 km from the famous Vindhyavasini temple. Ghamapur is now known as India's Greenwich.
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