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There are two reasons for taking 82 deg 30 min as the standard meridian:

1. it comes on the multiple of 7 deg and 30 min i.e. 7-30X15=82 deg 30min ie 30 minutes

2. it exactly lies in the middle of india ie 68 deg 7 min + 97 deg 25 min divided by 2= 82 deg 30 min

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It is becoz there is 1min. time difference on every degree
and india`s time is taken from the center line (bhumadye rekha) at Greenwich from 82.30 degree to arrang the time of india 
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