A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?
Correct Answer :
South
Solution :
The correct option is South.
To find the initial direction the person walked from his house, we can trace the path by assuming the initial direction is South and verify if the final position of the office relative to the house aligns with the North-East direction.
Let us represent the movements on a standard Cartesian coordinate plane where:
- The house is located at the origin:
- East represents the positive x-axis direction.
- West represents the negative x-axis direction.
- North represents the positive y-axis direction.
- South represents the negative y-axis direction.
Assuming the person starts walking South from his house:
1. First movement: Walks 100 m straight (South).
New position:
facing South.
2. Second movement: Turns left (which is East when facing South) and walks 100 m.
New position:
facing East.
3. Third movement: Turns left again (which is North when facing East) and walks 300 m.
New position:
facing North.
4. Fourth movement: Turns right (which is East when facing North) and walks 100 m to reach his office.
Final office position:
.
Now, let us analyze the final coordinates of the office:
relative to the house at:
Since both the x-coordinate (200 m East) and y-coordinate (200 m North) are positive and equal, the office is located exactly in the North-East direction from the house.
Since this matches the given condition that his office is exactly in the North-East direction, our assumption is correct. Therefore, the direction in which he walked initially from his house is South.
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