1) India lies between 68⁰7' and 97°25' east longitudes. the longitudinal extent of india is approximately 30 degrees.
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.