Bombay, and India generally, isn't the only place
chronometrically out of step with the rest of the world. Lots of countries,
particularly in Asia, are a half-hour out of sync, including Burma, Sri Lanka,
and Afghanistan.
Nepal is 40 minutes off the mark. Saudi Arabia, ever the trailblazer, has some
bizarre system in which clocks are supposedly reset to midnight every day at
sunset.
All of this traces back to the haphazard system of timekeeping prevalent before
the 1884 Washington conference that established Greenwich Mean Time (GMT) as the
international reference point.
Prior to this, people made use of "local mean time," i.e., they figured out
approximately when the sun was directly overhead, called that noon, and went
from there.
India, as it happens straddles two time zones, but for obvious reasons preferred
to have one uniform time throughout the country. Rather than choose between
GMT+5 and GMT+6
the government apparently decided to split the difference