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Keshav starts from Point A and drives 22 km towards the South. He then takes a left turn, drives 24 km, turns left and drives 27 km. He then takes a left turn and drives 25 km. He takes a final left turn, drives 5 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 degrees turns only unless specified)
3 km to the east
2 km to the east
1 km to the east
4 km to the east
1 km to the east
Track net movement by resolving horizontal and vertical displacements separately: Total Vertical = 22 (South) - 27 (North) = 5 km South; Total Horizontal = 24 (West) - 25 (East) - 5 (East) = 6 km East. Result: 1 km East.
Track net movement by resolving horizontal and vertical displacements separately: Total Vertical = 22 (South) - 27 (North) = 5 km South; Total Horizontal = 24 (West) - 25 (East) - 5 (East) = 6 km East. Result: 1 km East.
Mapping the Path
Starting at A(0,0): 1) South 22 km тЖТ (0, -22). 2) Left (East)тВВтВД km тЖТ (24, -22). 3) Left (North)тВВтВЗ km тЖТ (24, 5). 4) Left (West)тВВтВЕ km тЖТ (-1, 5). 5) Left (South)тВЕ km тЖТ (-1, 0).
Calculating Resultant Displacement
After all movements, the final position relative to A(0,0) is (-1, 0). This means Keshav is 1 km to the West of Point A.
Determining Final Return Direction
To return from (-1, 0) back to A(0, 0), Keshav must travel 1 km in the positive X direction, which is East.
A: 3 km East is incorrect as the final coordinate calc is 1 km. B: 2 km East is mathematically unsupported by the path summation. D: 4 km East exceeds the net displacement.
C is correct because the sequence of movements ends at a position 1 km West of the starting point, necessitating a 1 km move East to return.
Always convert direction-based puzzles into (x, y) coordinates on a grid to avoid errors in counting turns!
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