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Anmol starts from Point A and drives 23 km towards the west. He then takes a right turn, drives 27 km, turns right and drives 29 km. He then takes a right turn and drives 32 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┬░ turns only unless specified.)
3 km to the north
4 km to the north
5 km to the north
6 km to the north
3 km to the north
Track net displacement on X (West-East) and Y (North-South) axes separately. West/South = negative, East/North = positive. Sum them to find the gap.
Track net displacement on X (West-East) and Y (North-South) axes separately. West/South = negative, East/North = positive. Sum them to find the gap.
Establish Coordinates
Start at Point A (0,0). Move 23 km West: (-23, 0). Move Right (North) 27 km: (-23, 27).
Continue Path
Turn Right (East) 29 km: (6, 27). Turn Right (South) 32 km: (6, -5). Turn Right (West) 6 km: (0, -5).
Analyze Results
Point P is at (0, -5). Wait, re-evaluating: Move W 23 (-23, 0), N 27 (-23, 27), E 29 (6, 27), S 32 (6, -5), W 6 (0, -5). Distance to A(0,0) is 5km North. Re-reading turn sequences: West (-23,0), Right/North (27), Right/East (29), Right/South (32), Right/West (6). 6 units West from x=6 puts him at 0. -5 units North from y=27 puts him at -5. Correction: -23 + 29 - 6 = 0 (X-axis). 27 - 32 = -5 (Y-axis). The result is 5km North.
Verification
Correcting the path: West 23, Right (North) 27, Right (East) 29, Right (South) 32, Right (West) 6. Total West-East: -23 + 29 - 6 = 0. Total North-South: 27 - 32 = -5. He is 5km South of A. He needs to go 5km North to reach A.
B: 4km North is mathematically incorrect. C: 5km North is the correct displacement based on the final coordinates. D: 6km North is incorrect based on the path calculation.
C is correct because the final position of Anmol is 5 km South of Point A, requiring a movement of 5 km towards the North to return to the starting point.
Always draw a rough sketch on your rough sheet; treat East/North as positive (+) and West/South as negative (-) to solve direction problems in seconds.
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