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Pankaj starts from Point A and drives 12 km towards east. He then takes a left turn, drives 18 km, turns left and drives 19 km. He then takes a left turn and drives 21 km. He takes a final left turn, drives 7 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.)
1 km to the north
3 km to the north
4 km to the north
5 km to the north
3 km to the north
Track the net movement on the North-South and East-West axes separately: East-West is (12 - 19) = -7 (7 km West); North-South is (18 - 21 + 7) = 4 km North. Since he is 7 km West and 4 km North of A, he needs to cover the displacement, but in this specific turn sequence, simplify the net shift.
Track the net movement on the North-South and East-West axes separately: East-West is (12 - 19) = -7 (7 km West); North-South is (18 - 21 + 7) = 4 km North. Since he is 7 km West and 4 km North of A, he needs to cover the displacement, but in this specific turn sequence, simplify the net shift.
Define Coordinates
Let Point A be (0,0). Move 1: 12 km East = (+12, 0). Move 2: 18 km Left (North) = (+12, +18). Move 3: 19 km Left (West) = (12-19, 18) = (-7, 18). Move 4: 21 km Left (South) = (-7, 18-21) = (-7, -3). Move 5: 7 km Left (East) = (-7+7, -3) = (0, -3).
Analyze Final Position
After all moves, the final position P is (0, -3) relative to A(0,0). This means Point P is 3 km South of A.
Determine Direction to A
To return to Point A (0,0) from P (0, -3), Pankaj must move 3 km towards the North.
A: 1 km north is incorrect as total vertical displacement is 3 km. C: 4 km north is incorrect calculation of vertical axes (18 - 21 + 7). D: 5 km north is incorrect.
B is correct because the net displacement relative to the start point is 3 km South, meaning to reach A, he must travel 3 km North.
Always maintain a Cartesian grid (x,y) for multi-turn problems. It prevents confusion compared to visual drawing alone.
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