Reasoning — Direction and Distance

1. The person starts by walking North. 2. Turns right: From North, a right turn means facing East. 3. Walks 5m, still facing East. 4. Turns left: From East, a left turn means facing North. 5. Walks 10m, still facing North. Therefore, the person is facing North.

1. The man walks 5 km East from the starting point. 2. He then turns left. From East, a left turn means facing North. 3. He walks 3 km North. His final position is 5 km East and 3 km North of the starting point. Therefore, his final direction from the starting point is North-East.

Let's analyze the rotation: - South-East (SE) is 135 degrees clockwise from North. - North (N) is 0 degrees from North. - To change SE to N, we rotate 135 degrees anti-clockwise (or 225 degrees clockwise). Let's verify with the second condition: - North-East (NE) is 45 degrees clockwise from North. - West (W) is 270 degrees clockwise from North. - To change NE to W, we rotate 225 degrees clockwise (270 - 45 = 225). So, the rotation is 225 degrees clockwise for all directions. Now, apply this to West: - West (W) is 270 degrees clockwise from North. - Rotating 225 degrees clockwise from West: 270 + 225 = 495 degrees. - 495 - 360 = 135 degrees. - 135 degrees clockwise from North is South-East. Therefore, West will become South-East.

Let point A be at the origin (0,0). 1. Walks 8m South: Position (0, -8). Facing South. 2. Turns left (East) and walks 5m: Position (5, -8). Facing East. 3. Turns right (South) and walks 7m: Position (5, -8 - 7) = (5, -15). Facing South. 4. Turns right (West) and walks 5m: Position (5 - 5, -15) = (0, -15). Facing West. Point B is at (0, -15). Point A is at (0,0). The straight-line distance between A and B is the distance between (0,0) and (0,-15), which is 15m.

1. In the morning, after sunrise, the sun is in the East. 2. Therefore, shadows fall towards the West. 3. Meena's shadow is exactly to Reena's right. This means Reena's right side is West. 4. If a person's right side is West, then they must be facing South. Therefore, Reena was facing South.

1. At 12 noon, both the hour and minute hands normally point towards North. 2. In this clock, at 12 noon, the minute hand (and thus the hour hand) points towards North-East. 3. This means the entire directional setup is rotated 45 degrees clockwise (North becomes North-East). 4. At 6 PM, the hour hand normally points towards South. 5. Applying the 45-degree clockwise rotation to South: South (180°) + 45° = 225°. 6. 225 degrees corresponds to South-West. Therefore, at 6 PM, the hour hand will point towards South-West.

Let's set up a coordinate system with Point Q at the origin (0,0). 1. Point P is 10m East of Point Q: P = (10, 0). 2. Point R is 5m South of Point P: R = (10, -5). 3. Point S is 10m West of Point R: S = (10 - 10, -5) = (0, -5). 4. Point T is 8m North of Point S: T = (0, -5 + 8) = (0, 3). Point T is at (0,3) and Point Q is at (0,0). Since T has the same x-coordinate as Q and a positive y-coordinate, Point T is North of Point Q.

Let the starting point be (0,0). 1. Walks 10 km North: The position becomes (0, 10). 2. From there, walks 6 km South: The position becomes (0, 10 - 6) = (0, 4). 3. Then, walks 3 km towards East: The position becomes (3, 4). His final position is (3,4) relative to the starting point (0,0). Distance from starting point = √(3² + 4²) = √(9 + 16) = √25 = 5 km. Direction from (0,0) to (3,4) is North-East. Therefore, he is 5 km North-East from his starting point.

Let's set up a coordinate system with Point Y at the origin (0,0). 1. Point X is 10m North of Point Y: X = (0, 10). 2. Point Z is 10m East of Point Y: Z = (10, 0). 3. Point W is 5m North of Point Z: W = (10, 0 + 5) = (10, 5). 4. Point V is 10m West of Point W: V = (10 - 10, 5) = (0, 5). Now, we need to find the shortest distance between Point X (0,10) and Point V (0,5). Since both points have the same x-coordinate, the distance is simply the absolute difference in their y-coordinates. Distance = |10 - 5| = 5m.

Let the starting point O be at the origin (0,0). **Friend A's path:** 1. Walks 10 km North: A's position is (0, 10). 2. Turns right (East) and walks 5 km: A's final position is (0 + 5, 10) = (5, 10). **Friend B's path:** 1. Walks 5 km East: B's position is (5, 0). 2. Turns left (North) and walks 15 km: B's final position is (5, 0 + 15) = (5, 15). Now, we need to find the shortest distance between A (5,10) and B (5,15). Since both points have the same x-coordinate, the distance is the absolute difference in their y-coordinates. Distance = |15 - 10| = 5 km.