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To solve this type of question we require a logical approach.

Before proceeding to the solution, we will have to see the diagram of cardinal directions of the route.

Now let us see the diagram of two persons starting with their journey in their respective directions.

Person labelled 1 is starting the journey from south direction and Person labelled 2 is starting the journey along the south-east direction.

All the direction are straight lines. The North-South line is perpendicular to West-East line.

Now to find out which person reaches the destination first we will have to draw a straight line joining the south direction with south east direction in the following manner.

Now we have got a triangle OAB and the ∠ OAB = 90°.

Person 1 will travel along the side OA of the triangle and the Person 2 will travel along the side OB of the triangle.

Now let us apply the Pythagoras Theorem to Δ OAB.

OB is the hypotenuse of the triangle [side opposite to 90° is the hypotenuse of the triangle]

So OB² = OA² + AB²

Now when we look at the above equation we observe that length of OB is far greater than length OA.

So it is observed that Person 1 travelling along OA side that is along south direction will have a shorter distance to reach the distance.

At the same time Person 2 travelling along OB side will have longer distance to travel to reach the distance as both Person 1 and Person 2 are starting from same place.

Hence Person 1 will reach the distance first and Person 2 will reach after some time.