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The question is about the International Date Line which is basically the 180° meridian. When crossing the Date Line from east to west, we add 24 hours or 1 day, and when we cross it from west to east, we subtract 24 hours or 1 day. The ship sails from east to west crossing the 180° meridian. Therefore, the captain should subtract 24 hours or 1 day from the given time.
Option 1, January 1, 0030 hrs is correct because after crossing the 180° meridian at 2330 hrs, subtracting 24 hours from it brings the time back to 23:30 hrs of the previous day, January 1, 1999. Then, adding 1 hour to it, since the journey will last for an additional hour, will result in 0030 hrs of January 1,1999.
Option 2, January 2, 0030 hrs would be correct if the ship was sailing in opposite direction from west to east.
Options 3 and 4, January 3, 0030 hrs and January 4, 0030 hrs, are clearly incorrect as they denote dates well after the point of the crossing and the additional one-hour