Types of Distance and Direction Reasoning Questions
Passage Based
Angle Based
Shadow Based
Let’s understand each type in detail -
1) Passage-Based Distance and Direction Reasoning Questions
Example:
Directions: Kartik walks 40 m straight from his home towards the North. Then, he turns left and walks 25 m. He turns left again and walks 15 m. Finally, he turns left and walks 25 m to reach Point X. What is the shortest distance between his home and Point X?
1) 22 m
2) 25 m
3) 15 m
4) 55 m
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and Direction diagram]()
Point A is the starting point and X is the endpoint, so the distance between them is XA.
XA = 40 – 15 = 25
So, the shortest distance between Kartik's home and point X is 25 m. Hence, the second option is correct.
Example:
Directions: Bismita walks 200 m towards the East and then turns right and walks 210 m to reach a hospital. What is the shortest distance between the starting point and the hospital?
1) 310 m
2) 290 m
3) 220 m
4) 260 m
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and direction diagram]()
Here, A is the starting point and B is the endpoint.
For the shortest distance (AB) between the starting point and the endpoint,
With the help of Pythagoras' formula:
$\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2$,
⇒ $(AC)^2 + (BC)^2 = (AB)^2$
⇒ $(200)^2 + (210)^2 = (AB)^2$
⇒ $40000 + 44100 = (AB)^2$
⇒ $(AB)^2 = 84100$
⇒ $AB = 290$ m
So, the shortest distance between Bismita's starting point and the hospital is 290 m. Hence, the second option is correct.
2) Angle-Based Distance and Direction Reasoning Questions
In this question, the information is usually given in the angle way, like one has turned 90͒ / 45͒, and so on. Let’s, uh, understand it with an example-
Example:
Directions: A girl is standing facing towards the east. She turns 45 degrees in the anticlockwise direction and then turns 180 degrees in the clockwise direction. Which direction is she facing now?
1) West
2) South
3) North
4) South-West
Solution:
As per the given information, the direction the girl will look is as follows –
![Angle based Distance and Direction Diagram]()
Therefore, the girl is facing towards the southwest direction. Hence, the fourth option is correct.
3) Shadow-Based Distance and Direction Reasoning Questions
In shadow based direction questions, you have to remember that a shadow always lands on the opposite side of the Sun, like its sort of directly away from where the light is coming from. So, in the morning the shadow points to the west, then in the evening it shifts toward the east, and around noon 12 PM, it can be very small or even absent.
Example:
Directions: At the time of sunrise, Diksha and Arpita are sitting in a park with their backs facing each other. If the shadow of Diksha falls to the right of Arpita, then in which direction is Arpita facing?
1) North
2) East
3) West
4) South
Solution:
Given: At the time of sunrise, Diksha and Arpita are sitting in a park with their backs facing each other.
![Shadow based distance and direction diagram]()
At the time of Sunrise, the Sun is in the east direction, and the shadow will be in the west direction. So, it is given that the shadow is on the right side of Arpita. Therefore, Arpita will face towards the South direction.
Hence, the fourth option is correct.
Solved Examples of Distance and Directions
According to the different types, the practice questions for direction and distance are as follows -
1. Passage-based distance and direction questions
1. Directions: A person starts from point Z and moves 7 km towards the South. He turns right and moves 5 km, turns right and moves 3 km, then turns right and moves 1 km. He takes a left turn and moves 4 km to reach point X. How much and in which direction does he need to move now to reach point Z?
1) 4 km South
2) 4 km East
3) 4 km West
4) 6 km East
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and Direction Frame]()
Now, we have to find the direction and distance to reach the point Z.
![Distance and Direction Diagram]()
From the above diagram, the Z point is in the east direction and at a distance of (5 – 1) = 4km from point X. Hence, the second option is correct.
2. Directions: A boy walks 15 m north, turns right, and walks 20 m. Again, he turns right and walks 15 m. Finally, he turns to his left and moves 20 m. What is the distance now from his original position?
1) 40 m
2) 46 m
3) 50 m
4) 45 m
Solution:
According to the instructions given, the diagram is as follows –
![Distance and Direction Diagram]()
Here, O is the starting point and D is the finishing point, and OD is the total distance from the starting point.
OA = 15m; AB = 20m; BC = 15m; CD = 20m
And, OD = 20 + 20 = 40m
So, the distance now from his original position is 40m. Hence, the first option is correct.
3. Directions: Manoj starts from point A and drives X km towards the south and then turns left and drives Y km. He then takes a right turn and drives for 4 km to reach point D. If Manoj drove a total of 17 km between Points A and D, and both X and Y are perfect squares where X > Y, then what is the value of X?
1) 4 km
2) 11 km
3) 5 km
4) 9 km
Solution:
According to the instructions given, the diagram is as follows –
![Distance and Direction Frame]()
Now, we have to find the values of X and Y.
![Distance and Direction Diagram]()
Here, A is the starting point and D is the finishing point.
AB = X km; BC = Y km; CD = 4 km
And, the total distance between Points A and D is 17 km.
⇒ AD = AB + BC + CD
⇒ 17 = X + Y + 4
⇒ 17 – 4 = X + Y
⇒ 13 = X + Y
It is given that both X and Y are perfect squares where X > Y, so X = 9 km and Y = 4 km.
So, the value of X is 9 km. Hence, the fourth option is correct.
4. Directions: Starting from point A, an animal walked 15 m towards the East. It took a left turn and walked 25 m. Then, it took a right turn and walked 10 m. Again it took a left turn and walked 15 m. Finally, it took a left turn and walked 25 m. How far and in which direction is the animal now from the starting point A?
1) 25 m, East
2) 40 m, South
3) 40 m, North
4) 25 m, West
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and Direction Diagram]()
From the above diagram, the endpoint is in the north direction from the starting point and at a distance of 40 m. Hence, the fourth option is correct.
5. Directions: Starting from point X, a person walked 20 m towards the South to reach point Y. From there, he took a left turn and walked 25 m to reach point Z. He then took a left turn and walked for another 20 m to reach point P. What is the approximate shortest distance between the points X and Z and in which direction is the person's final position with respect to point X?
1) 50 m, South East
2) 36 m, South East
3) 32 m, East
4) 46 m, North West
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and Direction Frame]()
Now, we have to find the approximate shortest distance between points X and Z and in which direction is the person's final position with respect to point X.
![Distance and Direction Pythagoras Diagram]()
Here, X is the starting point, Z is the endpoint, and the shortest distance between points X and Z = d
Using Pythagoras' theorem, we have
⇒ $(d)^2 = (20)^2 + (25)^2$
⇒ $(d)^2 = 400 + 625$
⇒ $(d)2 = 1025$
⇒ $d = 32.01 ~ 32$
From the above diagram, the endpoint (P) is in the east direction from the starting point (X), and the shortest distance between points X and Z is 32m. Hence, the fourth option is correct.
2. Angle-based distance and direction questions
1. Directions: Joseph starts for his school from his house. He first goes 2 km towards the west and then turns 90° clockwise and goes further 2 km to reach his school. In which direction is his house from his school?
1) Southeast
2) South
3) Northwest
4) North
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Direction and Distance Frame]()
Now, we have to find the direction of the school with respect to the house.
![Distance and Direction Pythagoras Theorem]()
Therefore, the house is in the southeast direction with respect to the school. Hence, the first option is correct.
2. Directions: P started walking from north to south. She turned right at a right angle and then again right at a right angle. In which direction was she ultimately walking?
1) North
2) East
3) South
4) West
Solution:
Firstly, we will draw the direction and distance diagram according to the instructions –
![Direction and Distance Diagram Frame]()
Now, we have to find the direction in which P is moving.
![Distance and direction diagram]()
So, P was facing in the north direction. Hence, the first option is correct.
3. Directions: Starting from a point, a person travels 3 km towards the east and turns left and travels 4 km. Then again he turns to the left by 45° and moves straight. Which direction is he facing now?
1) North-East
2) North-West
3)South-East
4)South-West
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and Direction Diagram]()
Here, A is the starting point and D is the endpoint.
So, the person is facing in the northwest direction. Hence, the second option is correct.
4. Directions: Vijay walks 10 metres westward, then turns left and walks 10 metres. He then again turns left and walks 10 metres. He takes a 45° turn rightwards and walks straight. In which direction is he walking now?
1) South
2) West
3) South-East
4) South-West
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and Direction Diagram]()
Here, A is the starting point and E is the endpoint.
So, Vijay is walking in the southwest direction. Hence, the fourth option is correct.
5. Directions: Karan, facing south, moved straight 2 km and from there turned to his right 90° and travelled 2 km. Then he took a 45° turn to his left and travelled 1 km. Where would he be now concerning the starting point?
1) South Region
2) South-East Region
3) North-West Region
4) South-West Region
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Distance and Direction Frame]()
Now we have to find the direction of Karan concerning the starting point.
![Distance and Direction Diagram]()
So, Karan is in the South-West region concerning the starting point. Hence, the fourth option is correct.
3. Shadow-Based Distance and Direction Questions
1. Directions: John, in the morning, started walking towards the north and then turned towards the opposite side of the sun. He then turns left again and stops. Which direction is he facing now?
1) North
2) West
3) South
4) East
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Directions Frame]()
After walking towards the north direction, John turns toward the left direction (As the sun rises in the east direction and the opposite side of the east is west direction.)
![Distance and Direction Diagram]()
So, John is facing towards the south direction. Hence, the third option is correct.
2. Directions: One morning, Raju walked towards the sun. After some time, he turned left and again to his left. Which direction is he facing?
1) North
2) South
3) East
4) West
Solution:
Given: One morning, Raju walked towards the sun, i.e., he walked towards the east direction. (Because in the morning, the Sun is in the east direction.)
Firstly, we will draw the diagram as per the given instructions –![Directions Frame]()
Now, we have to find which direction Raju is facing.
![Distance and Direction Diagram]()
So, Raju is facing towards the west direction. Hence, the fourth option is correct.
3. Directions: Shama, during the time of sunset, started walking towards the opposite side of the sun and then she turned right and right again. What direction is she facing?
1) South
2) West
3) East
4) North
Solution:
Firstly, we will draw the direction and distance diagram according to the instructions given in the question
![Directions frame]()
Shama started walking towards the opposite direction of the sun during sunset, i.e., she was walking in the East direction (because during sunset, the sun is in the west direction).
![Distance and Direction Diagram]()
So, Shama is facing the west direction. Hence, the second option is correct.
4. Directions: One morning, Raju walked towards the sun. After some time, he turned left and again to his left. Which direction is he facing?
1) North
2) South
3) East
4) West
Solution:
Given: One morning, Raju walked towards the sun, i.e., he walked towards the east direction. (Because in the morning, the Sun is in the east direction.)
Firstly, we will draw the diagram as per the given instructions –
![Distance and direction frame]()
Now, we have to find which direction Raju is facing.
![Distance and Direction Diagram]()
So, Raju is facing towards the west direction. Hence, the fourth option is correct.
5. Directions: John, in the morning, started walking towards the north and then turned towards the opposite side of the sun. He then turns left again and stops. Which direction is he facing now?
1) North
2) West
3) South
4) East
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Directions frame]()
After walking towards the north direction, John turns toward the left direction (As the sun rises in the east direction and the opposite side of the east is the West direction.)
![Distance and Direction Diagram]()
So, John is facing towards the south direction. Hence, the third option is correct.
Distance and Directions Questions for SSC/ RRB exams
Q-1) Directions: Starting from a point, a person travels 3 km towards the east and turns left and travels 4 km. Then again he turns to the left by 45° and moves straight. Which direction is he facing now?
1) North-East
2) North-West
3) South-East
4) South-West
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Directions Frame]()
Here, A is the starting point and D is the endpoint.
![Distance and Direction Diagram]()
So, the person is facing in the northwest direction. Hence, the second option is correct.
Q-2) Directions: Rajneesh started walking towards the north. He took a left turn after walking 20 metres. He again took a right turn after walking 30 metres. Which direction is he facing now?
1) North
2) East
3) West
4) South
Solution:
Firstly, we will draw the diagram as per the given instructions –
![Directions Frame]()
Here, A is the starting point and D is the endpoint.
![Distance and Direction Diagram]()
So, Rajneesh is facing in the north direction. Hence, the first option is correct.
Step-by-Step Approach
First thing, figure out which way you begin, like north south east west, or whatever direction the question gives. Then track each movement as it happens, step by step, don’t just jump to the end. You write it down as you go, or at least keep a mental note of the changing sides. After that, draw a quick, simple diagram, just a line with turns, so the path doesn’t feel so abstract . Use arrows for the motion, and mark the corners, even if it looks a bit messy.
Then decide the final direction by looking at where you end up after all the turns. If the question asks for the shortest distance, you calculate that too, usually by breaking the route into a right angle shape.
Formula & Trick
Use the Pythagorean theorem to get the shortest distance when the movement forms something like a right-angled triangle .
$\text{Distance} = \text{Speed} \times \text{Time}$
But in many reasoning problems, speed and time aren’t given. So you switch strategies, and you count movements in steps, units, or blocks to get the total distance. For shortest path questions where the turns are right angles :
$\text{Shortest Distance} = \sqrt{(\Delta x)^2 + (\Delta y)^2}$
Example:
If a person walks 3 km east and then 4 km north, the shortest distance from the starting point is:
$\sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = 5 \ \text{km}$
Shortcut Methods for Quick Calculation
When you’re solving direction and distance questions with answers, you can save time with these little tricks:
Situation | Tip | Formula/Approach |
Movement in the same straight line | Add distances | $D = D_1 + D_2$ |
Movement in opposite directions | Subtract distances | $D = D_1-D_2$ |
Movement at right angles | Apply Pythagoras | $D = \sqrt{D_x^2 + D_y^2}$ |
Movement forming a rectangle | Use diagonal as shortest path | $D = \sqrt{\text{Length}^2 + \text{Width}^2}$ |
Tip: Always draw a little diagram when you’re solving. It helps you see the turn(s) and avoid errors in direction reasoning, like what goes where.