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The earth in it's rotation covers a distance of 1 degree longitude in 4 min. India has a longitudinal extent of 30 from Arunachal Pradesh(east) to Gujarat(west).It accounts for a time difference of 2 hours.So,the Sun rises two hours earlier in Arunachal Pradesh as compared to Gujarat.
      To avoid confusion due to time dfferences and to have a standard time for reference,the time along the meridian 82 degree 30 minE passing near Allahabad in U.P has been taken as the standard time for the entire country.That is why the clock shows the same time.
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1.The sun rises two hours earlier in arunachal pradesh as compared to gujarat.
2.It takes 4 minutes for the suns position to move 1 longitude.
3. This means that the time is different for each  degree of longitude.
4. Based on the longitudes the time is calculated.
5. Then two different places in our country will have different times. which causes lot of confusion.
6.To avoid this confusion of time from place to place 82 degrees 30 E longitude is taken as standard meridian of india and serves as indian standard time.
7.All people in india have to follow this time.This clocks show the same time.