Priya cycles 5 km towards the North from her starting point, then turns right to cycle 4 km towards the East.\nFrom there she turns right again and cycles 5 km towards the South, and finally she turns to her right once more and cycles 6 km.\nWhere is she now in relation to her starting position?

Introduction / Context:
This question describes a cyclist, Priya, travelling along a rectangular-like path with several right turns. We are asked to determine her final position with respect to the starting point. Problems of this type involve tracking stepwise movements in the North–South and East–West directions and then computing the net displacement. Recognizing when segments cancel each other is key to simplifying the final answer quickly.

Given Data / Assumptions:

• Priya starts from a fixed point.
• She cycles 5 km towards the North.
• Then she turns right and cycles 4 km towards the East.
• After that, she turns right again and cycles 5 km towards the South.
• Finally, she turns to her right and cycles 6 km.
• All turns described as “right” are 90 degree turns, and all stretches are straight-line segments.
• We use the usual convention that from facing North, a right turn leads to East; from East, right leads to South; and from South, right leads to West.

Concept / Approach:
We can model Priya's movement on a coordinate grid. North–South displacements affect the vertical coordinate, and East–West displacements affect the horizontal coordinate. Some movements may cancel out: for example, going 5 km North and then 5 km South returns her to the same North–South level. The final horizontal position can then be deduced by accumulating the Eastward and Westward displacements. This method avoids confusion and makes the final position clear without needing complex geometry.

Step-by-Step Solution:
Step 1: Assume Priya starts at (0, 0). Step 2: She cycles 5 km North to reach (0, 5). She is now facing North. Step 3: She turns right from North, which means she now faces East, and cycles 4 km to reach (4, 5). Step 4: From facing East, she turns right again to face South and cycles 5 km, reaching (4, 0). Step 5: From facing South, she turns right once more to face West and cycles 6 km, finally reaching (-2, 0). Step 6: The starting point is (0, 0), and the final position is (-2, 0). This means she is 2 km to the West of the starting point.

Verification / Alternative check:
We can verify by comparing net North–South and East–West movements separately. Total Northward distance is 5 km and total Southward distance is also 5 km, so North–South displacement is zero. For East–West, she goes 4 km East, then 6 km West. Net horizontal displacement = 6 km West − 4 km East = 2 km West. Since the vertical displacement is zero, her final position must be exactly 2 km West of the starting point, confirming the coordinate calculation.

Why Other Options Are Wrong:
2 km East reverses the actual direction; Priya ends up West, not East, of the start. 10 km West and 10 km East greatly exaggerate the net movement and ignore the cancellations that occur in the North–South and East–West directions. 6 km North would require a net positive vertical displacement, which does not happen here because the 5 km North and 5 km South movements cancel each other out completely.

Common Pitfalls:
Some learners mistakenly add all distances without considering direction, leading to incorrect large values such as 10 km or more. Others may misinterpret right turns, especially after multiple turns, or forget that opposite movements cancel out. Drawing the path on graph paper or mentally tracking the coordinates after each step is a reliable technique that reduces errors significantly in such direction sense questions.

Final Answer:
Priya's final position is 2 km West of her starting point.