Direction Sense

1. A. North-West
2. B. West
3. C. South
4. D. South-West

Answer: C

Explanation

Let’s assume the person initially walks North and trace the path:
1. Starts at (0,0), walks 100m North: (0, 100).
2. Turns left (now facing West), walks 100m: (-100, 100).
3. Turns left (now facing South), walks 300m: (-100, 100 – 300) = (-100, -200).
4. Turns right (now facing West), walks 100m: (-100 – 100, -200) = (-200, -200).
In this hypothetical scenario, the office is at (-200, -200) relative to the house (0,0), which is in the South-West direction.

The problem states that the office is actually in the North-East direction. South-West is exactly opposite to North-East (180 degrees apart).
This means our initial assumption for the starting direction was 180 degrees off. If assuming North led to South-West, then the actual starting direction must be 180 degrees opposite to North, which is South.

Let’s verify with an initial South direction:
1. Starts at (0,0), walks 100m South: (0, -100).
2. Turns left (now facing East), walks 100m: (100, -100).
3. Turns left (now facing North), walks 300m: (100, -100 + 300) = (100, 200).
4. Turns right (now facing East), walks 100m: (100 + 100, 200) = (200, 200).
The office is at (200, 200) relative to the house (0,0), which is indeed in the North-East direction. Thus, he initially walked South. This question tests direction sense and spatial reasoning.

1. A. South-West
2. B. South-East
3. C. North-West
4. D. North-East

Answer: D

Explanation

Let’s trace the person’s direction:
1. **Walks 100 m Westward**: The person is facing West.
2. **Turns left**: If facing West, a left turn means turning 90 degrees counter-clockwise. This changes the direction to South. The person is now facing South.
3. **Takes a 225-degree turn clockwise**: From facing South:
– A 90-degree clockwise turn from South leads to West.
– Another 90-degree clockwise turn from West leads to North. (Total 180 degrees clockwise).
– Remaining turn: 225 – 180 = 45 degrees clockwise.
– A 45-degree clockwise turn from North leads to North-East.

Alternatively, using degrees (North = 0°, East = 90°, South = 180°, West = 270°):
1. Starts facing West (270°).
2. Turns left (90° counter-clockwise): 270° – 90° = 180° (South).
3. Takes a 225° turn clockwise: 180° + 225° = 405°.
4. To find the final direction, subtract 360° (a full circle): 405° – 360° = 45°.
5. 45° corresponds to the North-East direction. This question tests direction sense and angular turns.