Two cars C and D start from the same point. Car C first travels 9 km towards the south, then turns to its left and travels another 11 km. Car D first travels 3 km towards the east, then turns towards the south and travels 5 km, and finally turns to its left and travels another 8 km. After completing these movements, where is car D located with respect to the final position of car C?

Introduction / Context:
In this direction sense test question, the movements of two cars are described using distances and turns. The task is to track both cars on an imaginary grid and then determine the relative position of car D with respect to car C. Such questions test spatial visualization, systematic plotting, and understanding of directions like north, south, east, and west.

Given Data / Assumptions:

• C and D start from the same origin point.
• Car C: 9 km south, then left turn, 11 km more.
• Car D: 3 km east, then 5 km south, then left turn, 8 km.
• Standard convention: north is up, south is down, east is right, west is left.

Concept / Approach:
We model movements on a coordinate plane. Take the starting point as (0, 0). Moving east increases the x coordinate, moving west decreases it, moving north increases the y coordinate, and moving south decreases it. After finding final coordinates of both cars, subtract the coordinates of C from those of D to find the relative displacement of D from C.

Step-by-Step Solution:
Set the starting point O as (0, 0). Car C moves 9 km south: C1 = (0, -9). From facing south, a left turn means facing east, so C moves 11 km east: C2 = (11, -9). Car D moves 3 km east: D1 = (3, 0). Then D moves 5 km south: D2 = (3, -5). From facing south, a left turn means facing east, so D moves 8 km east: D3 = (11, -5). Final coordinates: C at (11, -9) and D at (11, -5). Relative position of D from C = (11 - 11, -5 - (-9)) = (0, 4). This means D is 4 km directly north of C.

Verification / Alternative check:
Instead of coordinates, you can visualize the diagram. Both cars end up on the same vertical line (same east west level), but D has moved 4 km more towards the north than C. Therefore, D must be directly north of C, at a distance of 4 km.

Why Other Options Are Wrong:
Option A: 4 km South is opposite to the actual direction, because D is above C, not below.
Option B: 14 km North exaggerates the distance; the northward gap is only 4 km.
Option D: 14 km South is incorrect in both direction and distance.
Option E: None of these is incorrect because one of the given options exactly matches the correct answer.

Common Pitfalls:
Students often confuse left and right turns when facing south, or mix up absolute and relative positions. Another frequent error is comparing each car with the origin instead of comparing D with C. Using systematic coordinates or a quick rough sketch helps prevent mistakes in such reasoning problems.

Final Answer:
Car D is located 4 km North of the final position of car C.