Practice questions on direction sense problems involving displacement, turns, shadow-based direction clues, and calculating final direction and distance from a starting point
Question 1
Pankaj is facing west. He turns 45° in the clockwise direction and then again turns 180° in the same (clockwise) direction, after which he turns 270° in the anti-clockwise direction. Which direction is he facing now?
Explanation
West = 270° bearing. +45° (CW) = 315°. +180° (CW) = 495° = 135°. -270° (CCW) = 135 - 270 = -135° = 225°
225° bearing corresponds to South-West
225° bearing corresponds to South-West
Question 2
Kavita moved a distance of 60 metres towards the east. She then turned to the left and walked about 30 metres, turned left again and walked 50 metres. Finally, she turned to the right at an angle of 45°. In which direction was she moving finally?
Explanation
Start facing East. Turning left from East gives North, and turning left again from North gives West. Turning right (clockwise) by 45° from West (270°) gives 270° + 45° = 315°, which is North-West.
Question 3
Priya walked 3 km east of her house and then turned north, covering 6 km. Finally, she moved 5 km towards west and then again 2 km east. How far is she from her initial position?
Explanation
Starting at (0,0) with East and North as positive: East 3 km → (3,0). North 6 km → (3,6). West 5 km → (-2,6). East 2 km → (0,6). Distance from start = 6 km (due north).
Question 4
Facing towards North, Ravi walks 35 m. He then turns left and walks 55 m. He again turns left and walks 35 m. How far is he from his original position and towards which direction?
Explanation
North 35 m → left turn faces West, walks 55 m → left turn faces South, walks 35 m
The two 35 m legs (North then South) cancel out, leaving a net displacement of 55 m West
The two 35 m legs (North then South) cancel out, leaving a net displacement of 55 m West
Question 5
Ram starts moving from a point, facing East. After walking 15 m, he turns to his left and walks 25 m, before turning to his right. Then he walks a distance of 35 m, then turns to his right and stops after walking a further distance of 25 m. Find how far Ram is from his starting point.
Explanation
East 15 m: (15, 0). Left turn (North) 25 m: (15, 25). Right turn (East) 35 m: (50, 25). Right turn (South) 25 m: (50, 0)
Distance from start = √502 + 02 = 50 m
Distance from start = √502 + 02 = 50 m
Question 6
A man is facing towards East and turns through 45° clockwise, again 180° clockwise and then turns through 270° anti-clockwise. In which direction is he facing now?
Explanation
Total clockwise turn = 45° + 180° = 225°; then 270° anti-clockwise = -270°
Net turn = 225° - 270° = -45° (i.e. 45° anti-clockwise from East)
45° anti-clockwise from East = North-East
Net turn = 225° - 270° = -45° (i.e. 45° anti-clockwise from East)
45° anti-clockwise from East = North-East
Question 7
Seven villages A, B, C, D, E, F and G are situated as follows:
E is 2 km to the west of B
F is 2 km to the north of A
C is 1 km to the west of A
D is 2 km to the south of G
G is 2 km to the east of C
D is exactly in the middle of B and E.
Which two villages are the farthest from one another?
E is 2 km to the west of B
F is 2 km to the north of A
C is 1 km to the west of A
D is 2 km to the south of G
G is 2 km to the east of C
D is exactly in the middle of B and E.
Which two villages are the farthest from one another?
Explanation
Let A=(0,0). F=2km north of A: F=(0,2). C=1km west of A: C=(-1,0). G=2km east of C: G=(1,0). D=2km south of G: D=(1,-2).
D is the midpoint of B and E, and E is 2km west of B: solving gives B=(2,-2), E=(0,-2).
Checking each option: F-E=4, D-C≈2.83, F-B=√(4+16)≈4.47, G-E=√5≈2.24.
The farthest pair is F and B (≈4.47 km).
D is the midpoint of B and E, and E is 2km west of B: solving gives B=(2,-2), E=(0,-2).
Checking each option: F-E=4, D-C≈2.83, F-B=√(4+16)≈4.47, G-E=√5≈2.24.
The farthest pair is F and B (≈4.47 km).
Question 8
There are four towns P, Q, R and T. Q is to the South-west of P, R is to the east of Q and South-east of P, and T is to the north of R in line with QP. In which direction of P is T located?
Explanation
Let P=(0,0). Q is South-west of P: Q=(-1,-1). R is East of Q and South-east of P: R=(1,-1) (satisfies both).
T is North of R and on the line QP extended (the line y=x): with x=1 on that line, T=(1,1), which is indeed directly North of R=(1,-1).
T relative to P=(0,0): T=(1,1) → North-East
T is North of R and on the line QP extended (the line y=x): with x=1 on that line, T=(1,1), which is indeed directly North of R=(1,-1).
T relative to P=(0,0): T=(1,1) → North-East
Question 9
Gopal started from the house towards West. After walking a distance of 30 metres, he turned towards right and walked 20 metres. He then turned left and, moving a distance of 10 metres, turned to his left again and walked 40 metres. He now turned to the left and walked 5 metres. Finally, he turned to his left. In which direction was he walking now?
Explanation
Start facing West. Turn right → North. Turn left → West. Turn left → South. Turn left → East. Finally, turn left (no walk) → North.
He ends up facing North.
He ends up facing North.
Question 10
Rasik walked 20 m towards north. Then he turned right and walked 30 m. Then he turned right and walked 35 m. Then he turned left and walked 15 m. Finally, he turned left and walked 15 m. In which direction and how many metres is he from the starting position?
Explanation
Start (0,0), facing North. North 20: (0,20). Turn right (East), 30: (30,20). Turn right (South), 35: (30,-15). Turn left (East), 15: (45,-15). Turn left (North), 15: (45,0).
Final position (45,0) is 45 m due East of the start.
Final position (45,0) is 45 m due East of the start.
Question 11
A child is looking for his father. He went 90 meters to the east before turning to his right. He went 20 meters before turning to his right again to look for his father at his uncle's place 30 meters from this point. His father was not there. From there, he went 100 meters to his north before meeting his father in a street. How far did the son meet his father from the starting point?
Explanation
Track position from start (0,0): East 90m → (90,0). Turn right (South), 20m → (90,-20). Turn right (West), 30m → (60,-20). North 100m → (60,80).
Distance from start = √602 + 802 = √3600 + 6400 = √10000 = 100 m
Distance from start = √602 + 802 = √3600 + 6400 = √10000 = 100 m
Question 12
Raju starts from point A and walks 1 km towards south, turns left and walks 1 km. Then he turns left again and walks 1 km. Now he is facing?
Explanation
Start facing South. Turn left (from South, left turn = East). Turn left again (from East, left turn = North).
He is now facing North.
He is now facing North.
Question 13
A man is facing north. He turns 45 degrees in the clockwise direction and then another 180 degrees in the same direction and then 45 degrees in the anticlockwise direction. Find which direction he is facing now.
Explanation
Start facing North (0°). Turn 45° clockwise: 45°. Turn 180° clockwise: 45+180=225°. Turn 45° anticlockwise: 225-45=180°, which is South.
Question 14
P started from his house towards west. After walking a distance of 25 m, he turned to the right and walked 10 m. He then again turned to the right and walked 15 m. After this he is to turn right at 135° and to cover 30 m. In which direction should he go?
Explanation
Start facing West. Turn right → facing North, walk 10m. Turn right again → facing East, walk 15m. Turn right by 135° from East (bearing 90°): 90 + 135 = 225°, which is South-West.
Question 15
Ravi left home and cycled 10 km towards South, then turned right and cycled 5 km, and then again turned right and cycled 10 km. After this he turned left and cycled 10 km. How many kilometres will he have to cycle to reach his home straight?
Explanation
Start (0,0) facing South, walk 10: (0,-10). Turn right (West), walk 5: (-5,-10). Turn right (North), walk 10: (-5,0). Turn left (West), walk 10: (-15,0).
Distance back to home (0,0) from (-15,0) = 15 km
Distance back to home (0,0) from (-15,0) = 15 km
Question 16
Read the information given below to answer these questions. A, B, C, D, E, F, G, H and I are nine houses. C is 2 km east of B. A is 1 km north of B and H is 2 km south of A. G is 1 km west of H while D is 3 km east of G and F is 2 km north of G. I is situated just in the middle of B and C while E is just in the middle of H and D.
Distance between E and I is:
Distance between E and I is:
Explanation
Let B=(0,0). C=2km east of B: C=(2,0). A=1km north of B: A=(0,1). H=2km south of A: H=(0,-1). G=1km west of H: G=(-1,-1). D=3km east of G: D=(2,-1).
I = midpoint of B and C = (1,0). E = midpoint of H and D = (1,-1).
Distance E to I = √02 + 12 = 1 km
I = midpoint of B and C = (1,0). E = midpoint of H and D = (1,-1).
Distance E to I = √02 + 12 = 1 km
Question 17
Pooja drove 7 km towards the North, turned right and drove 5 km, turned left and drove 3 km, and then turned right and drove 19 km. How far is she from her starting point?
Explanation
North 7 km, East 5 km, North 3 km, then East 19 km. She ends 5 + 19 = 24 km East and 7 + 3 = 10 km North of the start.
Distance = √(242 + 102) = √676 = 26 km.
Distance = √(242 + 102) = √676 = 26 km.
Question 18
Anil walked 4 km towards the West, turned right and walked 3 km, turned left and walked 8 km, and then turned left and walked 3 km. How far is he from his starting point?
Explanation
West 4 km, North 3 km (right from West), West 8 km (left from North), then South 3 km (left from West). The North and South walks cancel, so he is 4 + 8 = 12 km West of the start.
Question 19
Tara walked 15 m from point M to point N. She turned right and walked 6 m, turned right again and walked 15 m, and then turned right and walked 6 m. How far is she now from M?
Explanation
The four walks of 15 m, 6 m, 15 m and 6 m, each after a right turn, trace a rectangle. She ends exactly where she started, so she is 0 m from M.
Question 20
Kunal walked 12 m from point X to point Y. He then turned left and walked 5 m, turned left again and walked 12 m, and finally turned left and walked 2 m. How far is he now from X?
Explanation
Take X at (0, 0) and Y at (12, 0). A left turn gives 5 m to (12, 5); another left turn gives 12 m back to (0, 5); a final left turn gives 2 m towards X, to (0, 3). He is 3 m from X.
Question 21
P is to the north of Q, and R is to the east of P. In which direction is Q with respect to R?
Explanation
Place Q at the origin. P is north of Q, and R is east of P, so R is north-east of Q. Therefore Q is South-West of R.
Question 22
Four houses A, B, C and D are in the same area. House C is to the south of A and to the west of B. House B is to the north of D. In which direction is D with respect to A?
Explanation
Place A at the origin. C is south of A. B is east of C, so B is south-east of A. D is south of B, so D is further south and also east of A. So D is South-East of A.
Question 23
A girl went 32 m towards the South, turned left and went 24 m, then turned left again and went 12 m to reach her aunt's house. Her mother was not there. From there she went 12 m South and met her mother. How far from the starting point did she meet her mother?
Explanation
Take the start as (0, 0). South 32 m gives (0, −32); East 24 m gives (24, −32); North 12 m gives the aunt's house at (24, −20).
South 12 m brings her back to (24, −32).
Distance = √(242 + 322) = √1600 = 40 m.
South 12 m brings her back to (24, −32).
Distance = √(242 + 322) = √1600 = 40 m.
Question 24
A boy walked 50 m towards the North to look for his father. He turned right and walked 40 m, then turned right again and walked 20 m to reach a shop. His father was not there. From the shop he went 20 m East and then 50 m North, where he met his father. How far from the starting point did he meet his father?
Explanation
Take the start as (0, 0). North 50 m gives (0, 50); East 40 m gives (40, 50); South 20 m gives the shop at (40, 30).
Then East 20 m gives (60, 30) and North 50 m gives (60, 80).
Distance = √(602 + 802) = √10000 = 100 m.
Then East 20 m gives (60, 30) and North 50 m gives (60, 80).
Distance = √(602 + 802) = √10000 = 100 m.
Question 25
One morning after sunrise, Geeta stood facing a lamp post. The shadow of the post fell exactly behind her. In which direction was she facing?
Explanation
In the morning the sun is in the East, so shadows fall towards the West. The shadow falls behind her, so West is behind her and she is facing East.
Question 26
One evening before sunset, Ramesh was standing facing a tree. The shadow of the tree fell exactly to his left. In which direction was he facing?
Explanation
In the evening the sun is in the West, so shadows fall towards the East. The shadow is on his left, so East is on his left, which means he is facing South.
Question 27
If P # Q means P is to the east of Q, P @ Q means P is to the north of Q, P $ Q means P is to the south of Q, and P & Q means P is to the west of Q, then in M $ N & O @ P, in which direction is P with respect to N?
Explanation
M $ N: M is south of N. N & O: N is west of O. O @ P: O is north of P.
Place N at the origin. O is to the east of N, and P is to the south of O.
So P lies to the east and to the south of N: P is South-East of N.
Place N at the origin. O is to the east of N, and P is to the south of O.
So P lies to the east and to the south of N: P is South-East of N.
Question 28
If P # Q means P is to the east of Q, P @ Q means P is to the north of Q, P $ Q means P is to the south of Q, and P & Q means P is to the west of Q, then in A @ B # C $ D, in which direction is D with respect to B?
Explanation
A @ B: A is north of B. B # C: B is east of C. C $ D: C is south of D.
Place C at the origin. Then B is to the east of C and D is to the north of C.
From B, D lies to the north and to the west, so D is North-West of B.
Place C at the origin. Then B is to the east of C and D is to the north of C.
From B, D lies to the north and to the west, so D is North-West of B.
Question 29
One morning after sunrise, Kavya and Leela were talking face to face. Leela's shadow fell exactly behind Kavya. In which direction was Leela facing?
Explanation
In the morning the sun is in the East, so shadows fall towards the West. Leela's shadow falls behind Kavya, so West is behind Kavya and Kavya is facing East. Leela faces Kavya, so Leela is facing West.
Question 30
One evening before sunset, Arun and Bala were standing face to face. Arun's shadow fell exactly to Bala's left. In which direction was Bala facing?
Explanation
In the evening the sun is in the West, so shadows fall towards the East. Arun's shadow is on Bala's left, so East is on Bala's left. A person with East on the left is facing South.
Question 31
Farah walked 10 m towards the South, then turned left and walked 24 m, and turned left again and walked 17 m. How far is she from her starting point?
Explanation
South 10 m, East 24 m (left from South), then North 17 m (left from East). She ends 24 m East and 17 − 10 = 7 m North of the start.
Distance = √(242 + 72) = √625 = 25 m.
Distance = √(242 + 72) = √625 = 25 m.
Question 32
Nikhil walked 12 m towards the East. He then turned left and walked 9 m, and turned left again and walked 24 m. How far is he from his starting point?
Explanation
East 12 m, North 9 m (left from East), then West 24 m (left from North). He ends 24 − 12 = 12 m West and 9 m North of the start.
Distance = √(122 + 92) = √225 = 15 m.
Distance = √(122 + 92) = √225 = 15 m.
Question 33
Asha left home and walked 8 km towards the North. She turned right and walked 6 km, turned right again and walked 8 km, and then turned left and walked 4 km. How far is she from home?
Explanation
North 8 km, then East 6 km, then South 8 km brings her back level with home, 6 km to the East. Turning left from South faces East, so she walks 4 km more to the East. She is 6 + 4 = 10 km from home.
Question 34
Raj walked 5 km, turned right and walked 2 km, then turned right again and walked 7 km. He was now walking towards the South. In which direction did he start walking?
Explanation
Work backwards. He finally walked South after a right turn, so before that he was walking East. He reached East by a right turn, so he was first walking North. So he started walking towards the North.
Question 35
After walking 4 km, Meena turned left and walked 3 km. She then turned right and walked 6 km. At the end she was walking towards the West. In which direction did she start walking?
Explanation
Work backwards from the last direction. She was finally walking West after a right turn, so before that turn she was walking South (a right turn from South faces West). She reached South by a left turn, so she was first walking West (a left turn from West faces South). So she started walking towards the West.
Question 36
Sourav walks 20 meters towards North. He then turns left and walks 40 meters. He again turns left and walks 20 meters. Further, he moves 20 meters after turning to the right. How far is he from his original position?
Explanation
Take North as up. Sourav walks 20 m north, turns left and walks 40 m west, turns left and walks 20 m south, then turns right (west) and walks 20 m.
His position: 20 m north - 20 m south = 0 north-south, and 40 + 20 = 60 m west.
He is 60 m from his original position.
His position: 20 m north - 20 m south = 0 north-south, and 40 + 20 = 60 m west.
He is 60 m from his original position.
