Shaurya walks 3 km towards the east and then turns to his left and walks for 4 km. He again turns left and walks 6 km. How far (shortest distance) and in which direction is he now from his starting point?

1. A

   5 km north-west

2. B

   7 km north

3. C

   5 km west

4. D

   7 km north-east

Appeared in: AIIMS BHOPAL NO- 2018( Shift-2nd)

Explanation

• Shaurya's final position is 3 km West and 4 km North of his starting point.
• The shortest distance is the hypotenuse of a right-angled triangle with sides 3 km and 4 km.
• Using the Pythagorean theorem, the distance is calculated as √(3² + 4²) = √(9 + 16) = √25 = 5 km.
• Since his final position is to the West (horizontal displacement) and North (vertical displacement) of the start, the resulting direction is North-West.

Why Other Options Were Wrong

• Option B: This answer incorrectly calculates the distance by adding the first two legs of the journey (3 km + 4 km = 7 km) and misinterprets the final direction.
• Option C: This option correctly calculates the distance as 5 km but fails to account for the 4 km northward movement, resulting in an incorrect direction.
• Option D: This option is incorrect in both distance and direction. The distance is calculated incorrectly (perhaps by adding 3+4), and the direction is wrong as the final movement was westward, not eastward.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Direction and Distance Reasoning as background academic context rather than a clinical decision trigger.
• This question type is not directly related to clinical nursing practice.
• However, it assesses logical reasoning and spatial awareness, which are foundational skills for problem-solving in any professional environment, including healthcare.
• For example, a nurse might use similar spatial reasoning to navigate a large hospital complex or to position equipment correctly in a patient's room.

How to Approach the Question

• First, identify the starting point and the cardinal directions (North, South, East, West).
• Trace the path step-by-step, keeping track of the movements along the East-West (horizontal) and North-South (vertical) axes.
• Calculate the net horizontal displacement: 3 km East - 6 km West = 3 km West.
• Calculate the net vertical displacement: 4 km North.
• Use the Pythagorean theorem (a² + b² = c²) with the net horizontal and vertical displacements to find the shortest distance (the hypotenuse).
• Determine the final direction based on the net displacements (e.g., West and North combine to form North-West).

Concept Tested & Keywords

• Concept Tested: Direction and Distance Reasoning
• Stem keywords: walks, east, left, north, west, shortest distance, direction, starting point
• Lead-in keywords: How far, in which direction

Question ID

Q2EicjW0qTRKDdosIGOnnF

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