Shakti starts from Point A and drives 22 km towards South. He then takes a left turn, drives 20 km, turns left

Question

Shakti starts from Point A and drives 22 km towards South. He then takes a left turn, drives 20 km, turns left and drives 12 km. He then takes a left turn and drives 17 km. He takes a final right turn, drives 10 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again?(All turns are 90 degree turns only unless otherwise specified.)

Examoogle · Accepted Answer

The correct answer is Option C: 3 km towards West. Track net X and Y displacements: Net Y = -22 + 12 + 10 = 0 (same horizontal plane as A). Net X = 20 - 17 = 3 km East. To return to A, move 3 km West.

Step-by-Step Solution & Concepts:
Shortcut Trick: Track net X and Y displacements: Net Y = -22 + 12 + 10 = 0 (same horizontal plane as A). Net X = 20 - 17 = 3 km East. To return to A, move 3 km West.

Steps: Mapping the Path: Start at A(0,0). Move South 22km (0, -22). Left turn (East) 20km (20, -22). Left turn (North) 12km (20, -10). Left turn (West) 17km (3, -10). Right turn (North) 10km (3, 0). Point P is at (3, 0).. Calculating Resultant: Point A is at (0,0) and Point P is at (3,0). The displacement is 3 km East. To return from P(3,0) to A(0,0), Shakti must move 3 km West.

Answer: C is correct because Point P is located 3 km East of Point A, so traveling 3 km West is the shortest path to return to Point A.

Why options are wrong: A: 3km South is incorrect as P is on the same Y-axis level as A. B: 4km North is incorrect as it would move him away from the Y=0 line. D: 2km East would increase the distance from A.

Exam Tip: In direction puzzles, always use a grid or (x,y) coordinates to avoid confusion from multiple turns; 'North' is +Y, 'South' is -Y, 'East' is +X, 'West' is -X.

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