I don't know astronomy that well, but I am preparing for the second stage of IJSO, and here in India they do add some questions like these ones.

A star is seen rising from Kolkata (23.5N 92 E) at 7 pm IST. What time can it be seen rising from Mumbai (19N 72E)?

If someone could explain how I might go about solving this, and some surrounding theory so I can grasp the concept, I'll be really grateful.

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    $\begingroup$ As stated, it would be hard to determine. You need to know the declination of the star to answer properly. So unless your star is on the celestial equator, or your two observing points are on the same parallel, i'd say there's a missing piece of information to perform the calculation. $\endgroup$ – FSimardGIS Jan 22 '19 at 17:57
  • $\begingroup$ Well this was the question and it also had an answer in the answer key...idk..thanks tho $\endgroup$ – Sujal Patel Jan 23 '19 at 4:24
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    $\begingroup$ And what is the answer they stated? Do they simply use the difference in longitude for the calculation? $\endgroup$ – FSimardGIS Jan 23 '19 at 15:13
  • $\begingroup$ the answer is given 8 20 pm $\endgroup$ – Sujal Patel Jan 24 '19 at 16:04
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    $\begingroup$ Apparently, only the difference in longitude is taken into account... 20 degrees corresponds to 80 minutes and 7pm +80min = 8h 20min... $\endgroup$ – Tosic Jan 24 '19 at 16:17

"Time" in astronomy has many meanings. In essence, let us look at something called Sidereal Time.

On a fixed day, the difference between local and sidereal time is roughly the same. Sidereal time is the sum of the star's right ascension (constant) and its hour angle. The rising hour angle is given by the expression

$$\arccos(-\tan (p) \tan(d)),$$

where p is the latitude and d is the declination.

Since the latitude is "roughly" the same we only need to take longitude into account. This means that the time when an event happens, since it happens at the same sidereal time happens $S_2-S_1$ (S are local sidereal times) later in the second city (the difference is roughly the same since the difference between local and sidereal times is constant for this day).

Now, it happens 80 minutes later since 20 degrees to 360 is 80 min to 24h.

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