Correct Answer: (b) January 2, 00:30 hr
Solution:Aleutian Island's eastern end lies at the West of 180° Meridian, (172° East longitude) while Dutch Harbour lies at East side of 180º Meridian i.e at (166°31'55" West longitude). As the movement of the ship from West to East of 180 Meridian, the date will lag behind by 1 day. So, on 23:30 hr. January 1999 crossing 180 Meridian by rule the date should be 31 December 1998 and after 1 hour (23.30+60=2400+ 30) captain of the ship will record 00:30 hr. 1 January, 1999, But actually, the International Date Line does not completely follow the 180 Meridian to avoid segregating the places with equal political and the economic entity (including Aleutian Islands and Dutch Harbour). In the content of this situation International Date Line is even not crossed by the ship and the day will be same even after 1 hour captain of the ship will record 00:30 hr. 2 January, 1999.