Difficulty: Medium
Correct Answer: 10 km West
Explanation:
Introduction / Context:
This problem belongs to the standard direction sense category in verbal reasoning. Such questions test whether a student can mentally track movements on the ground using cardinal directions and turns, and then convert that mental path into a final relative position from the starting point. These questions are very common in bank exams, SSC, railway exams and other competitive tests, so mastering the basic technique is very helpful.
Given Data / Assumptions:
Concept / Approach:
The most reliable method is to imagine or sketch a simple coordinate system. We treat the starting point as (0, 0). Movement towards the north increases the y coordinate, movement towards the south decreases it. Movement towards the east increases the x coordinate and movement towards the west decreases it. After plotting every leg of the journey, we compare the final coordinates with the origin and read off how far and in which direction the courier has moved from the start.
Step-by-Step Solution:
Step 1: Place the courier at the origin, which we mark as (0, 0).Step 2: He rides 6 km south. South means the y coordinate decreases. New position becomes (0, -6).Step 3: From there he turns towards the west and rides 2 km. West means x decreases. New position becomes (-2, -6).Step 4: At this point he turns to his right. When someone is facing west, a right turn means facing north. Riding 6 km north increases the y coordinate by 6. Position becomes (-2, 0).Step 5: Finally he turns again towards the west and rides 8 km. Moving 8 km west decreases the x coordinate by 8. The final position becomes (-10, 0).Step 6: The starting point was (0, 0). The final point is (-10, 0). This means he is 10 km away along the west direction from the starting point.
Verification / Alternative check:
We can also check without coordinates by grouping vertical and horizontal movements separately. In the vertical direction, he goes 6 km south and later 6 km north, so these cancel each other out, bringing him back to the same north south level as the start. In the horizontal direction he moves 2 km west and later 8 km more west, which gives a total of 10 km west. Since there is no eastward movement to balance this, he must finish 10 km west of the origin. This confirms our coordinate based result.
Why Other Options Are Wrong:
Option B (6 km West) ignores the final extra 8 km west movement and treats only the first horizontal leg. Option C (10 km East) reverses the correct direction, confusing west with east. Option D (6 km East) is inconsistent with every leg of the path, because there is no eastward motion at all in the description. Only the option that places him 10 km to the west of his starting point matches the net displacement.
Common Pitfalls:
Students often make mistakes when interpreting a right turn from a given facing direction. Right from west is north, not south. Another frequent error is to add distances without considering sign and cancellation. For example, some may simply add all numbers and misinterpret 6, 2, 6, and 8 as a single linear distance. The safe approach is always to separate horizontal and vertical components and ensure that movements in opposite directions are netted properly. Drawing a quick rough diagram on paper helps many aspirants avoid confusion.
Final Answer:
The courier delivery person ends up 10 km to the west of his starting position, so the correct option is “10 km West”.
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