A street seller starts from his home and pushes his cart 1 km towards the east, then turns towards the north and walks 4 km, then turns towards the west and walks 9 km and finally turns to his left and walks 4 km. Where is he with respect to his home now?

Introduction / Context:
This question tracks the path of a street seller who starts from his home and walks in a rectangular pattern. We are asked for his final position relative to his home, specifically in terms of direction and distance. The situation is a straightforward application of net horizontal and vertical displacement where some legs cancel each other.

Given Data / Assumptions:
- He starts from home at an origin point. - First he walks 1 km east. - Then he walks 4 km north. - Then he walks 9 km west. - Finally he turns left from facing west, which means he faces south, and walks 4 km. - Movements are along straight lines on level ground.

Concept / Approach:
We interpret the movements using a coordinate system with east as positive x and north as positive y. The key observation here is that the northward and southward legs are equal and cancel, leaving only a net horizontal displacement. We compute the net horizontal movement by subtracting eastward distance from westward distance, which directly gives the displacement from home.

Step-by-Step Solution:
1. Start at (0, 0) representing the home. 2. Move 1 km east to reach (1, 0). 3. Move 4 km north to reach (1, 4). 4. Move 9 km west to reach (-8, 4) because 1 - 9 = -8. 5. Facing west, turn left to face south and move 4 km to reach (-8, 0). 6. The final position (-8, 0) is 8 km west of the origin (0, 0).

Verification / Alternative check:
Compute net movements directly. Horizontally, the seller walks 1 km east and 9 km west. Net movement equals 9 - 1 = 8 km west. Vertically, he walks 4 km north and 4 km south, so those movements cancel out completely, leaving zero net vertical movement. A rectangle drawn with up and down sides of equal length visually confirms that he ends up directly west of the home by 8 km.

Why Other Options Are Wrong:
- 10 km West of his home overestimates the net horizontal displacement; the net is only 8 km. - 8 km East and 10 km East assume he ended up on the opposite side of the origin. - Back at his home would require net horizontal and vertical displacements to be zero, which they are not.

Common Pitfalls:
Some candidates may misinterpret the final left turn, forgetting that turning left from facing west leads south, not north. Others may forget to subtract eastward movement from westward movement and instead simply add distances. Keeping track of facing direction at each step and writing separate totals for east, west, north and south helps avoid these mistakes.

Final Answer:
The street seller is 8 km west of his home.