An aeroplane takes off from 30° North Latitude, 50° East Longitude, and lands at the opposite end of the earth. Where does it land ?

The antipode (opposite point on the Earth's surface) of any location is directly opposite through the Earth's center; latitude changes hemisphere (sign) while longitude is shifted by 180° and normalized to the opposite E/W hemisphere [1]. Applying this to 30°N, 50°E: latitude becomes 30°S and longitude becomes 50°E + 180° = 230°, which normalized to the −180…+180° range is 130°W. Therefore the antipodal coordinates are 30°S, 130°W, matching option 4.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 5: Earths Magnetic Field (Geomagnetic Field) > 5.5. Magnetic Poles > p. 72