Question 1
Suresh started walking 4 km west from his office. Then he turned right and walked 2 km. Again he turned right and walked 2 km to reach his house. In which direction is Suresh's house from his office?
Explanation
Taking the office as the origin (0,0), with East as +x and North as +y:
Walk 4 km West: (-4, 0). Facing West, a right turn faces North; walk 2 km North: (-4, 2). Facing North, a right turn faces East; walk 2 km East: (-2, 2).
The house at (-2, 2) is 2 units West and 2 units North of the office -- equal magnitudes in both the West and North directions places it exactly in the North-West direction.
Walk 4 km West: (-4, 0). Facing West, a right turn faces North; walk 2 km North: (-4, 2). Facing North, a right turn faces East; walk 2 km East: (-2, 2).
The house at (-2, 2) is 2 units West and 2 units North of the office -- equal magnitudes in both the West and North directions places it exactly in the North-West direction.
Question 2
Mr. PQR walked 50 metres towards east, took a right turn and walked 40 metres. Then he took a left turn and walked 30 metres. In which direction is he now from the starting point?
Explanation
Starting at (0,0), with East as +x and North as +y:
Walk 50 m East: (50, 0). Facing East, a right turn faces South; walk 40 m South: (50, -40). Facing South, a left turn faces East; walk 30 m East: (80, -40).
The final position (80, -40) is East (positive x) and South (negative y) of the start, in roughly equal measure of direction -- placing him in the South-East direction from the starting point.
Walk 50 m East: (50, 0). Facing East, a right turn faces South; walk 40 m South: (50, -40). Facing South, a left turn faces East; walk 30 m East: (80, -40).
The final position (80, -40) is East (positive x) and South (negative y) of the start, in roughly equal measure of direction -- placing him in the South-East direction from the starting point.
Question 3
Starting from point A, PQ walked 40 metres south. She turned left and walked 40 metres. She then turned left and walked 40 metres. She again turned left and walked 60 metres and reached point B. How far and in which direction is the point B from the point A?
Explanation
Starting at A = (0,0), with East as +x and North as +y:
Walk 40 m South: (0, -40). Facing South, a left turn faces East; walk 40 m East: (40, -40). Facing East, a left turn faces North; walk 40 m North: (40, 0). Facing North, a left turn faces West; walk 60 m West: (40-60, 0) = (-20, 0).
Point B = (-20, 0) is 20 metres West of point A.
Walk 40 m South: (0, -40). Facing South, a left turn faces East; walk 40 m East: (40, -40). Facing East, a left turn faces North; walk 40 m North: (40, 0). Facing North, a left turn faces West; walk 60 m West: (40-60, 0) = (-20, 0).
Point B = (-20, 0) is 20 metres West of point A.
Question 4
Two persons, P and Q, start walking from a meeting point towards North. After walking 100 metres, P turns left and Q turns right. P, after walking 50 metres, takes a left turn and walks 150 metres. But Q walks 30 metres, turns to his right and walks 90 metres. What is the shortest distance between P and Q now in metres?
Explanation
Starting at (0,0), with East as +x and North as +y:
P's path: North 100 m: (0,100). Facing North, left turn faces West; walk 50 m West: (-50,100). Facing West, left turn faces South; walk 150 m South: (-50,-50).
Q's path: North 100 m: (0,100). Facing North, right turn faces East; walk 30 m East: (30,100). Facing East, right turn faces South; walk 90 m South: (30,10).
Distance between P(-50,-50) and Q(30,10): horizontal difference = 30-(-50) = 80, vertical difference = 10-(-50) = 60.
Shortest distance = √802 + 602 = √6400+3600 = √10000 = 100 metres.
P's path: North 100 m: (0,100). Facing North, left turn faces West; walk 50 m West: (-50,100). Facing West, left turn faces South; walk 150 m South: (-50,-50).
Q's path: North 100 m: (0,100). Facing North, right turn faces East; walk 30 m East: (30,100). Facing East, right turn faces South; walk 90 m South: (30,10).
Distance between P(-50,-50) and Q(30,10): horizontal difference = 30-(-50) = 80, vertical difference = 10-(-50) = 60.
Shortest distance = √802 + 602 = √6400+3600 = √10000 = 100 metres.
Question 5
A hunter is chasing a deer, by running 200 metres in east direction, turns to his right, runs 100 metres and turns to his right, runs 90 metres. Turning to his left, he runs 50 metres and then turns to left, runs 120 metres. Finally, he turns to left and runs 60 metres. He finds the deer in front of him at 100 metres. In which direction is the hunter standing with respect to the deer now?
Explanation
Track only the hunter's facing direction through each turn, starting facing East:
Right turn (from East) → facing South.
Right turn (from South) → facing West.
Left turn (from West) → facing South.
Left turn (from South) → facing East.
Left turn (from East) → facing North.
So by the end, the hunter is facing North, and the deer is 100 m directly ahead of him, i.e. to his North. This means the hunter, relative to the deer, is standing to the South.
Right turn (from East) → facing South.
Right turn (from South) → facing West.
Left turn (from West) → facing South.
Left turn (from South) → facing East.
Left turn (from East) → facing North.
So by the end, the hunter is facing North, and the deer is 100 m directly ahead of him, i.e. to his North. This means the hunter, relative to the deer, is standing to the South.
Question 6
Mr. ABC started walking down a road in the evening while facing the sun. After walking for a distance, he turned to his left, and then he turned to his right. In which direction is he facing now?
Explanation
In the evening, the sun is in the West, so Mr. ABC starts facing West.
Turning left from West faces him South. Turning right from South faces him West again.
So he is facing West.
Turning left from West faces him South. Turning right from South faces him West again.
So he is facing West.
Question 7
A boy is facing East. Turning to the right, he goes 20 m, then turning to the left he goes 20 m and turning to the right, he goes 20 m, then again turning to the right, he goes 40 m and then again he goes 40 m to the right. In which direction is he from his original position?
Explanation
Start facing East at origin (0,0). Turn right (now facing South), walk 20 m: (0,-20).
Turn left (now facing East), walk 20 m: (20,-20).
Turn right (now facing South), walk 20 m: (20,-40).
Turn right (now facing West), walk 40 m: (-20,-40).
Turn right (now facing North), walk 40 m: (-20,0).
Final position (-20,0) relative to start (0,0) is 20 m due West.
Turn left (now facing East), walk 20 m: (20,-20).
Turn right (now facing South), walk 20 m: (20,-40).
Turn right (now facing West), walk 40 m: (-20,-40).
Turn right (now facing North), walk 40 m: (-20,0).
Final position (-20,0) relative to start (0,0) is 20 m due West.
Question 8
A man drives 10 km towards north; from there he turns towards right and drives 3 km, then he takes a right turn and drives 6 km. How far and in which direction is he with reference to the starting point?
Explanation
Start at (0,0). Drive 10 km North: (0,10). Turn right (facing East), drive 3 km: (3,10). Turn right (facing South), drive 6 km: (3,4).
Displacement from start: 3 km East, 4 km North.
Distance = √32 + 42 = √25 = 5 km, in the North-East direction (since he is both east and north of the start).
Displacement from start: 3 km East, 4 km North.
Distance = √32 + 42 = √25 = 5 km, in the North-East direction (since he is both east and north of the start).
Question 9
Mr. Q walks 20 km north, then walks 14 km south, and then walks 8 km east. How far is he from his starting point?
Explanation
Start at (0,0). Walk 20 km North: (0,20). Walk 14 km South: (0,6). Walk 8 km East: (8,6).
Distance from start = √82 + 62 = √64 + 36 = √100 = 10 km.
Distance from start = √82 + 62 = √64 + 36 = √100 = 10 km.
Question 10
If West is replaced with North-East, then South will be replaced by which of the following directions?
Explanation
West is being rotated 135° clockwise (from West to North-East is a shift of three positions clockwise on the 8-point compass, i.e. 3 × 45° = 135°).
Applying the same 135° clockwise rotation to South: South → South-West → West → North-West.
So South is replaced by North-West.
Applying the same 135° clockwise rotation to South: South → South-West → West → North-West.
So South is replaced by North-West.
Question 11
Anil's house faces east. From the back-side of the house, he walks straight 50 meters, then turns to the right and walks 50 meters. Finally, he turns towards left and stops after walking 25 meters. Now, in which direction is Anil from the starting point?
Explanation
Since the house faces East, its back side opens to the West, so Anil starts walking West.
Start (0,0). Walk 50 m West: (-50, 0). Turn right (now facing North), walk 50 m: (-50, 50). Turn left (now facing West), walk 25 m: (-75, 50).
Final position (-75, 50) is west and north of the start, i.e. North-West.
Start (0,0). Walk 50 m West: (-50, 0). Turn right (now facing North), walk 50 m: (-50, 50). Turn left (now facing West), walk 25 m: (-75, 50).
Final position (-75, 50) is west and north of the start, i.e. North-West.
Question 12
If A x B means A is to the south of B; A + B means A is to the north of B; A % B means A is to the east of B; A - B means A is to the west of B; then in P % Q + R - S, in which direction is S with respect to Q?
Explanation
Reading the chain from the right: R - S means R is west of S, so let S = (0,0), R = (-1, 0).
Q + R means Q is north of R, so Q = (-1, 1).
P % Q means P is east of Q, so P = (0, 1) (not needed for this question).
S relative to Q: S - Q = (0 - (-1), 0 - 1) = (1, -1), i.e. east and south of Q -- South-East.
Q + R means Q is north of R, so Q = (-1, 1).
P % Q means P is east of Q, so P = (0, 1) (not needed for this question).
S relative to Q: S - Q = (0 - (-1), 0 - 1) = (1, -1), i.e. east and south of Q -- South-East.