A woman in a shopping complex starts from a certain point and walks 250 metres towards the east. Then she turns towards the north and walks 100 metres. Next she turns towards the west and walks 120 metres. Finally she turns to her left and walks another 100 metres. Where is she now with respect to her starting position?

Introduction / Context:
This problem is another example of a direction sense and displacement question where a person follows a rectangular or nearly rectangular path with turns at right angles. We must determine the final position of the woman relative to where she started, focusing on net horizontal and vertical movement rather than the total distance actually walked. Such questions test both understanding of directions (north, south, east, west) and basic coordinate or geometric reasoning.

Given Data / Assumptions:

• The woman starts at a certain point in a shopping complex.
• She walks 250 metres towards the east.
• She then turns north and walks 100 metres.
• Next she turns west and walks 120 metres.
• Finally she turns to her left and walks 100 metres.
• All turns are at right angles.
• We need her final position relative to the starting point in terms of both distance and direction.

Concept / Approach:
To solve, we use a coordinate grid. Let east be positive x, west be negative x, north be positive y and south be negative y. Each movement changes either the x coordinate or the y coordinate. After tracking all movements, we subtract the initial coordinates from the final coordinates to find net displacement. Because the final and initial y coordinates may cancel out, the net displacement often lies along one axis, making the direction easy to identify.

Step-by-Step Solution:
Step 1: Place the starting point at (0, 0). Step 2: The woman walks 250 metres east. This changes her x coordinate by +250, so her position becomes (250, 0). Step 3: She then turns north and walks 100 metres. This changes her y coordinate by +100, so her position becomes (250, 100). Step 4: Next she turns west and walks 120 metres, changing x by -120. Her new position is (130, 100). Step 5: Finally she turns left from facing west, which means she now faces south, and walks 100 metres. This changes y by -100, so her final position is (130, 0). Step 6: The final coordinates are (130, 0), which is 130 metres east of the origin and exactly on the same east-west axis.

Verification / Alternative check:
We can also reason without full coordinates by looking at horizontal and vertical movements separately. Horizontally, she first goes 250 metres east, then later 120 metres west. Net horizontal movement = 250 minus 120 = 130 metres east. Vertically, she goes 100 metres north and later 100 metres south, which cancel each other, leaving zero net vertical displacement. Therefore her final position must be 130 metres to the east of her starting point, confirming the coordinate method.

Why Other Options Are Wrong:

• Option B, 130 metres West, reverses the actual horizontal direction.
• Option C, 370 metres East, is obtained by incorrectly adding 250 and 120 without considering that the 120 metres is towards the west.
• Option D, 370 metres West, is doubly incorrect because it both adds wrongly and uses the wrong direction.
• Option E, 250 metres North, ignores the cancellation of vertical movements and treats only the first vertical leg.

Common Pitfalls:
A typical error is to add all east and west movements without considering signs, which gives a value like 370 in the wrong direction. Another mistake is to forget that the final left turn from west leads to south, not north. Keeping a small rough sketch or table of net east-west and north-south movements is an efficient way to avoid confusion and quickly determine the correct displacement and direction.

Final Answer:
The woman is now located 130 metres East of her starting position.