The longitudinal extent of India is 68° 7'E to 97° 24'E. By convention, the longitudes which serve as standard meridians for the country’s times should be multiples of 7°30’. Within the given longitudes, and should lie closest to the central longitude of the country. The central longitude is 83°15’. The only multiple of 7°30’, which fulfils the criteria, is the IST- 82°30’.

Hence, A is correct.