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The Indian Standard Time is calculated from the Allahabad observatory. Allahabad has 82.5°E longitude which corresponds to an exact 5 hours and 30 minutes difference between India and Greenwich, the reference point for GMT.
India's time zones were established in 1884. However at that time there were two standard time zones, Bombay Time and Calcutta Time. The IST came into effect in 1905. However, Bombay still persisted with its own time zone, 39 minutes behind IST, until 1955.
There is no daylight savings time in India.
People from India will tell you that IST actually stands for Indian Stretchable Time, a reference to the tendency of Indians to be late to almost everything.
Time zones