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Examoogle • User • info@examoogle.com • EE-2024-8821
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Farooque starts from Point A and drives 26 km towards East. He then takes a right turn, drives 17 km, turns right and drives 32 km. He then takes a right turn and drives 22 km. He takes a final right turn, drives 6 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 specified.)
6 km to the South
5 km to the South
5 km to the North
6 km to the North
5 km to the South
Quick Trick: Track net displacements on East-West (X) and North-South (Y) axes independently: X = (26 East + 32 East = 58 East), Y = (17 North - 22 South + 6 South = 1 South).
Track net displacements on East-West (X) and North-South (Y) axes independently: X = (26 East + 32 East = 58 East), Y = (17 North - 22 South + 6 South = 1 South).
Coordinate Mapping
Starting at Origin (0,0): 1) 26km East (+26, 0). 2) Right turn 17km South (+26, -17). 3) Right turn 32km West (-6, -17). 4) Right turn 22km North (-6, 5). 5) Final Right turn 6km East (0, 5).
Final Analysis
Wait, correcting the trace: A(0,0) -> 26E (26,0) -> 17S (26,-17) -> 32W (-6,-17) -> 22N (-6,5) -> 6E (0,5). Point P is at (0,5). To reach A(0,0) from (0,5), one must go 5km South.
A: 6 km South is incorrect as it overshoots the 5 km vertical distance. C: 5 km North would take him further from the horizontal axis. D: 6 km North is incorrect in both distance and direction.
B is correct because the final position is 5 km North of Point A, necessitating a move of 5 km to the South to return to the origin.
In multi-turn direction puzzles, always assign + and - values to N/S and E/W movements to simplify complex pathing into simple arithmetic.