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1) India lies between 68⁰7' and 97°25' east longitudes. the longitudinal extent of india is approximately 30 degrees.
2) the earth takes 4 min to sun's positions to move 1⁰ of longitude( 360 longitudes ÷24 hours = 4 min ). india has 30 longitudes approximately 30×4 = 120 min or 2 hours.
3) so sun rises 2 hours earlier in arunachal pradesh compared to gujarat ( if we travel east to west ). so inorder to avoid confusion of time from place we have choosen 82°30' as the standard meridian .
4)the standard meridian of india passes near allahabad serves as the standard meridian for the whole country.
5)  hence, the watches also show the same time.
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