Directions and Distance - Notes | UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making PDF Download

What is Direction and Distance?

• Direction and Distance questions involve solving puzzles related to distances and directions. Candidates are required to determine the final direction from the starting point and/or calculate the distance covered based on the provided distance and direction information.
• To successfully tackle direction and distance reasoning questions, candidates must be familiar with the cardinal directions, which include East, West, North, and South, as well as the intermediate or sub-directions: North-East, North-West, South-East, and South-West.
• Additionally, the direction and distance reasoning section often includes inquiries about right turns and left turns. It's essential to note that the direction of a right turn is always clockwise, while the direction of a left turn is always counterclockwise.

Important Concepts

There are four main directions - East, West, North and South as shown below:

There are four cardinal directions - North-East (N-E), North-West (N-W), South-East (S-E), and South-West (S-W) as shown below:

1. At the time of sunrise if a man stands facing the east, his shadow will be towards west.
2. At the time of sunset the shadow of an object is always in the east.
3. If a man stands facing the North, at the time of sunrise his shadow will be towards his left and at the time of sunset it will be towards his right.
4. At 12:00 noon, the rays of the sun are vertically downward hence there will be no shadow.

Types of Direction and Distance Reasoning

As now we know what consists of the questions related to the Direction and Distance reasoning section, let us see the various types of Direction and Distance questions below. 

1. Turns and Rotations 
In these types of Distance and Direction Reasoning Questions, rotations such as clockwise or anticlockwise, and turns such as left or right taken by people will be given and candidates will need to find his/her final position.

2. Distance and Displacement
A displacement is a short distance between the initial and final position of a point or a person. It quantifies both distance and direction. For example, if a person starts walking from a point and after walking 100m, reaches the same point from where he started then the displacement of that person is 0, whereas the distance travelled by him is 100m.

3. Shadow Based

In this types of Distance and Direction Reasoning, Questions are asked based on shadow. Shadows always fall on the opposite side of the Sun. For example, from sunrise to afternoon, such as before 12 PM, the shadow will fall in the west direction, whereas from afternoon to evening, such as after 12 PM, the shadow will fall in the east direction. No shadow will be formed at 12 PM. 

4. Coded Directions and Distance 

In these types of Distance and Direction Reasoning Questions, distance and directions are given in coded form and using the coded expression given in the question, candidates need to decode it and find the final answer. 

5. Direction Puzzle

In these types of Distance and Direction Reasoning Questions, persons or elements are arranged in a row and then move them in different directions.

Main types of questions are given below:

Type 1:

Siva starting from his house, goes 5 km in the East, then he turns to his left and goes 4 km. Finally he turns to his left and goes 5 km. Now how far is he from his house and in what direction?

Solution:

From third position it is clear he is 4 km from his house and is in North direction.

Type 2:

Suresh starting from his house, goes 4 km in the East, then he turns to his right and goes 3 km. What minimum distance will be covered by him to come back to his house?

Type 3:

One morning after sunrise Juhi while going to school met Lalli at Boring road crossing. Lalli's shadow was exactly to the right of Juhi. If they were face to face, which direction was Juhi facing?

Solution: In the morning sunrises in the east.

So in morning the shadow falls towards the west.

Now Lalli's shadow falls to the right of the Juhi. Hence Juhi is facing South.

Type 4:

Hema starting from her house walked 5 km to reach the crossing of Palace. In which direction she was going, a road opposite to this direction goes to Hospital. The road to the right goes to station. If the road which goes to station is just opposite to the road which IT-Park, then in which direction to Hema is the road which goes to IT-Park?

Solution:

From II it is clear that the road which goes to IT-Park is left to Hema

Sample Questions

Given below are sample direction and distance reasoning questions with answers to help you better understand the concepts behind it:

Question 1: Renu is facing south, She turns 90 degree left, then she turns 90 degree right, then she turns 180 degree left. Now in which direction is she facing?
Solution: If we analyse the question then according to the question Renu should be facing North right now. North is the correct answer. 

Question 2: Harry starts walking from his home, after walking 7 KM towards East he takes right and walks for another 8 KM. Now he turns 135 degrees right and walks for 2 KM and stops. What is the direction of the initial point with respect to the final stop point?
Solution: According to the question, if we draw the diagram we get North-West. So the correct answer is North-West. 

Question 3: A Nurse moved 90 m in the East in a hospital to look for her duty doctor, then she turned right and went 20m. After this she turned right and after going 30 m she reached I.C.U but the Doctor was not there. From there she went 100 m to her north and met her doctor. What distance did she move to meet her duty doctor from the starting point? 
Solution: If we use the Pythagoras formula, then we get 

H^2 = B^2 + P^2

H^2 = 60^2 + 80^2

H^2 = 10000

H = 100

So the answer is 100 m. 

 Question 4: On evening at 4 PM, Seeta and Reema are sitting in a garden facing each other. If Reema’s shadow falls behind her, which direction is Seeta facing? 
Solution: If we draw directions according to the given information we get, In the evening the Sun is in the West. Hence, the shadow falls on the East. Since, Reema’s shadow falls behind her. It implies that Reema is facing the West side. As Seeta and Reema are facing each other, So Seeta will face East. 

Question 5: In the morning a guy walks X km North, takes left and walks 3 KM, takes left and walks 5 KM, takes left and walks 5 KM and finally takes a right and walks 4 KM. Now his shadows are exactly pointing towards his initial position. What is the value of X?  
Solution: If we draw the directions then we get, X = 5 + 4 = 9 KM. Therefore, the correct answer is 4. 

Tips and Tricks 

• To resolve these types of questions, candidates need to know about the directions, there are 4 main directions and four sub directions. The main directions are; East, West, North, and South, whereas the sub directions are: North-East, North-West, South-East, and South-West. 
• Besides this, the right turn and left turn are generally asked in the direction and distance reasoning section. The direction of the right turn is always clockwise whereas the direction of the left turn is always anticlockwise. 
• To find the shortest distance covered between a starting point and the end point, candidates need to use the Pythagoras formula such as H^2 = B^2 + P^2, where H is the hypotenuse, B is the Base, and P is the Perpendicular. 
• Always use NESW in a clockwise direction. North is opposite to South and East is opposite to West.