Answers

2014-06-06T19:02:40+05:30
It is becuase the two places are quite far from each other... (two ends of india) that the sun rises at different time... but because of the IST , we follow the time of new delhi all over the india instead of local times...hence the difference

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2014-06-06T20:09:14+05:30
India is a large country. Therefore there is a difference in time in different locations in India. This cause many confusions in time of different locations. For avoiding these confusions in a large country like India, a standard time is used which is followed by every part of that country. This standard time in India is known as IST(Indian Standard Time). This IST passes through Allahabad which lies almost in the middle of India. This IST is the time of Allahabad at that time.
The actual time in Arunachal Pradesh is different from actual time in Gujrat (with respect to location of sun) but the time is same when talking about IST.
This IST is not the actual time of Arunachal Pradesh or Gujrat but it is the standard time of India(taken as time of Allahabad).
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Hoping that this will make your concept clear.