Why has been IST chosen as 82.5 degree East which lies near allahabad?

Time zone extends to difference in longitude of 15 degrees.

so from greenwich meridian to 7.5 degrees East longitude and 7.5 degrees west longitude, entire belt maintains GMT.
fron 7.5 deg east to 22.5 deg east longitude the belt will maintain GMT + 1 hour.
so u see the next belt will be 22.5 to 37.5 east = GMT + 2 hrs
then 37.5 to 52.5 east = GMT + 3 hrs
52.5 to 67.5 east longitude = GMT + 4 hrs
67.5 to 82.5 east longitude = GMT + 5 hrs
and 82.5 to 97.5 east longitude belt = GMT + 6 hours.
so u see the zone changes at longitude of 82.5, passing through allahabad.
as india spans breadth wise in two zones
the time zone to west of allahabad wud be GMT + 5 hrs and all places to east of allahabad will hv to maintain GMT + 6 hrs.

Britishers in their wisdom, knowing the illeteracy level in India at that time thought the common man wud get cofused, when to change the time.
so they chose allahabad longitide as the standard longitude for the purpose of maintaining time. the zone time was now chosen as between 5 and 6 hrs ahead of GMT.
Hence IST = GMT + 5.5 Hrs

International waters

Ships at sea in international waters should set their clocks according to the natural zone time. This is defined as follows. A 'zone' runs from -7.5 degrees to +7.5 degrees around a zone meridian. A zone meridian is an integer number of 15 degrees. For each zone easterly from the 0-zone 1 hour is added to the UTC time, and for each zone westerly 1 hour is subtracted. Within a zone the time offset is constant. Clocks are changed as is convenient, usually on a whole hour, when crossing a natural zone time boundary. As soon as the territorial waters of a nation is reached, the clock is set to the local time of that (part of the) nation. The international date line has no effect; only the 180° meridian.The following table lists all zones as a function of the longitude.

Longitude (°)	zone time		Longitude (°)	zone time
7.5E - 7.5W	0		7.5W - 7.5E	0
7.5W - 22.5W	-1		7.5E - 22.5E	1
22.5W - 37.5W	-2		22.5E - 37.5E	2
37.5W - 52.5W	-3		37.5E - 52.5E	3
52.5W - 67.5W	-4		52.5E - 67.5E	4
67.5W - 82.5W	-5		67.5E - 82.5E	5
82.5W - 97.5W	-6		82.5E - 97.5E	6
97.5W - 112.5W	-7		97.5E - 112.5E	7
112.5W - 127.5W	-8		112.5E - 127.5E	8
127.5W - 142.5W	-9		127.5E - 142.5E	9
142.5W - 157.5W	-10		142.5E - 157.5E	10
157.5W - 172.5W	-11		157.5E - 172.5E	11
172.5W - 180W	-12		172.5E - 180E	12

This can be expressed as an algorithm:
Longitude: east is positive, west is negative.
if (longitude >= 0): zone time = integerPart((longitude + 7.5)/15)
if (longitude < 0): zone time = -integerPart((-longitude + 7.5)/15)

What is the distance between a degree of latitude and longitude?

Degrees of latitude are parallel so the distance between each degree remains almost constant but since degrees of longitude are farthest apart at the equator and converge at the poles, their distance varies greatly.

Each degree of latitude is approximately 69 miles (111 kilometers) apart. The range varies (due to the earth's slightly ellipsoid shape) from 68.703 miles (110.567 km) at the equator to 69.407 (111.699 km) at the poles. This is convenient because each minute (1/60th of a degree) is approximately one mile.

A degree of longitude is widest at the equator at 69.172 miles (111.321) and gradually shrinks to zero at the poles. At 40° north or south the distance between a degree of longitude is 53 miles (85 km).

References: in.yahoo.com, http://home.tiscali.nl , http://geography.about.com/