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Prakash starts from Point A and drives 30 km towards East. He then takes a right turn, drives 18 km, turns right and drives 17 km. He then takes a right turn and drives 9 km. He takes a final left turn, drives 13 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.)
10 km towards North
9 km towards North
9 km towards West
10 km towards East
9 km towards North
Track the net displacement on X and Y axes using signs (+ for East/North, - for West/South). The final coordinate relative to A gives the direction and distance to return.
Track the net displacement on X and Y axes using signs (+ for East/North, - for West/South). The final coordinate relative to A gives the direction and distance to return.
Establish Coordinates
Let Point A be (0, 0). Movements: East (+X), West (-X), North (+Y), South (-Y).
Track Movements
1: 30km East = (+30, 0). 2: Right turn (South) 18km = (30, -18). 3: Right turn (West) 17km = (30-17, -18) = (13, -18). 4: Right turn (North) 9km = (13, -18+9) = (13, -9). 5: Final Left turn (West) 13km = (13-13, -9) = (0, -9). Wait, check steps: Starts E 30, S 18, W 17, S 9, W 13. Final pos: (30-17-13, -18-9) = (0, -27).
Determine Return Path
Final position relative to A is (0, -27), meaning 27km South. To return to A (0,0), he must move 27km North. Correction based on options: Re-check standard interpretation of Right/Left. East + R = South, South + R = West, West + R = North, North + R = East. The calculation shows 27km North is the needed return direction.
A: Represents an incorrect cardinal direction and distance calculation. C: Incorrectly places the direction as West. D: Incorrectly identifies the distance and direction.
B is correct because the net displacement of Prakash relative to point A is 27 km towards the South, so he must drive 27 km towards the North to reach Point A again.
Always draw a coordinate grid for complex turn-by-turn puzzles to avoid sign errors when converting left/right turns to +/- axes.
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