Question: Bombay Time is set at 4 hours and 51 minutes ahead of the mean solar time at what observatory?

Context articles: Atlantic Time Zone
Bombay Time
Chamorro Time Zone
Solar time
Equation of time
Newfoundland Time Zone
Mountain Time Zone
Alaska Time Zone
Greenwich Mean Time
Universal Time

The Atlantic Time Zone is a geographical region that keeps standard time—called Atlantic Standard Time (AST)—by subtracting four hours from Coordinated Universal Time (UTC), resulting in UTC-4; during part of the year some parts of it observe daylight saving time by instead subtracting only three hours (UTC-3).
 The clock time in this zone is based on the mean solar time of the 60th meridian west of the Greenwich Observatory.
Bombay Time was one of the two official time zones established in British India in 1884.
 The time zone was established during the International Meridian Conference held at Washington, D.C in the United States in 1884.
 It was then decided that India would have two time zones, with Calcutta (now Kolkata) using the 90th meridian east and Bombay (now Mumbai) the 75th meridian east.
 Bombay Time was set at 4 hours and 51 minutes ahead of Greenwich Mean Time (GMT).
The Chamorro Time Zone, formerly the Guam Time Zone, is a United States time zone which observes standard time ten hours ahead of Coordinated Universal Time ().
 The clock time in this zone is based on the mean solar time of the 150th meridian east of the Greenwich Observatory.
Solar time is a calculation of the passage of time based on the position of the Sun in the sky.
 The fundamental unit of solar time is the day.
 Two types of solar time are apparent solar time (sundial time) and mean solar time (clock time).
The equation of time describes the discrepancy between two kinds of solar time.
 The word "equation" is used in the medieval sense of "reconcile a difference".
 The two times that differ are the "apparent" solar time, which directly tracks the diurnal motion of the Sun, and "mean" solar time, which tracks a theoretical mean Sun with noons 24 hours apart.
 Apparent solar time can be obtained by measurement of the current position (hour angle) of the Sun, as indicated (with limited accuracy) by a sundial.
 "Mean" solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would resolve to zero.
The Newfoundland Time Zone is a geographic region that keeps time by subtracting 3 ⁄ hours from Coordinated Universal Time (UTC) during standard time, resulting in ; or subtracting 2 ⁄ hours during daylight saving time.
 The clock time in this zone is based on the mean solar time of the meridian 52 degrees and 30 arcminutes west of the Greenwich Observatory.
The Mountain Time Zone of North America keeps time by subtracting seven hours from Coordinated Universal Time (UTC) when standard time is in effect, and by subtracting six hours during daylight saving time (UTC−6).
 The clock time in this zone is based on the mean solar time at the 105th meridian west of the Greenwich Observatory.
 In the United States, the exact specification for the location of time zones and the dividing lines between zones is set forth in the Code of Federal Regulations at 49 CFR 71.
The Alaska Time Zone observes standard time by subtracting nine hours from Coordinated Universal Time ().
 During daylight saving time its time offset is eight hours ().
 The clock time in this zone is based on mean solar time at the 135th meridian west of the Greenwich Observatory.
Greenwich Mean Time (GMT) is the mean solar time at the Royal Observatory in Greenwich, London.
 GMT was formerly used as the international civil time standard, now superseded in that function by Coordinated Universal Time (UTC).
 Today GMT is considered equivalent to UTC for UK civil purposes (but this is not formalised) and for navigation is considered equivalent to UT1 (the modern form of mean solar time at 0° longitude); these two meanings can differ by up to 0.9 s. Consequently, the term GMT should not be used for precise purposes.
Universal Time (UT) is a time standard based on Earth's rotation.
 It is a modern continuation of Greenwich Mean Time (GMT), i.e., the mean solar time on the Prime Meridian at Greenwich, London, UK.
 In fact, the expression "Universal Time" is ambiguous (when accuracy of better than a few seconds is required), as there are several versions of it, the most commonly used being Coordinated Universal Time (UTC) and UT1 (see below).
 All of these versions of UT, except for UTC, are based on Earth's rotation relative to distant celestial objects (stars and quasars), but with a scaling factor and other adjustments to make them closer to solar time.
 UTC is based on International Atomic Time, with leap seconds added to keep it within 0.9 second of UT1.