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All questions of Distance & Direction for CUET Commerce Exam

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Sonu started from his house and walked 3 km Eastward, then he turned right and walked 2 km, then again he turned left and walked 1 km.  Again he turned left and walked 3 km, then turned right and walked 2 km. He turned right again and walked 1 km and reached his school. What is the shortest distance between Sonu's house and his school?
  • a)
    12 km                                                     
  • b)
    9km   
  • c)
    5 km                                                       
  • d)
    6 km   
Correct answer is option 'D'. Can you explain this answer?

Vertex Academy answered
To solve this, let's break down Hemant's movements step by step and visualize his path:
  1. Hemant starts from his house and walks 3 km eastward.
  2. He turns right and walks 2 km south.
  3. He turns left and walks 1 km east.
  4. He turns right and walks 2 km south.
  5. He turns right and walks 1 km west and reaches his school.
Now, let's consider the overall east-west and north-south movement:
  • East-West: Hemant initially walked 3 km east, then 1 km east, and finally 1 km west. So, the net eastward distance is 3 + 1 − 1 = 3 km.
  • North-South: Hemant walked 2 km south, then another 2 km south, so he walked a total of 2 + 2 = 4 km south.
The minimum distance from Hemant’s house to the school can be found using the Pythagorean theorem (since he moved in perpendicular directions):

Thus, the minimum distance between Hemant’s house and his school is: D: 5 km

A starts from his house and moves towards B’s house which is 4km North.  After walking for three-fourth of the distance he finds B coming towards him along with C, who is A’s enemy. Wanting to avoid him, A takes a left turn and runs for a distance of 2kms.Now, if from this point (say ‘P’) he decides to go to B’s house

How far is A, from his own house?

A. √5km   

B. √3km            

C. √7km            

D. √13km        

Correct answer is option is 'D'. Can you explain this answer?            

Vertex Academy answered
1. A walks three-fourths of the distance towards B's house, which is:
(3/4) × 4 km = 3 km (north).
After walking 3 km north, A takes a left turn and runs 2 km west.
2. Now, we have a right-angled triangle, where:
- One leg (north) = 3 km,
- Another leg (west) = 2 km.
3. The distance from A’s current position (P) to his house is the hypotenuse of this right-angled triangle:
Distance = √(3² + 2²) = √(9 + 4) = √13 km.
Thus, the distance from A’s current position to his own house is √13 km.

Sushant started from his house and walked 5km north of his house. Then he turned left and walked 3km, then he turned right and walked 5km. Again he turned right and walked 3km. Where is his final destination from his house?
  • a)
    Back to his house                 
  • b)
    7.5 km North-West
  • c)
    7.5 km North-East               
  • d)
    10 km North
Correct answer is option 'D'. Can you explain this answer?

Vertex Academy answered
To solve this question, let's analyze Sushant's path step-by-step based on the directions provided:
  1. Sushant starts at his house and walks 5 km north.
  2. He then turns left and walks 3 km west.
  3. Next, he turns right and walks 5 km north again.
  4. Finally, he turns right and walks 3 km east.
Now let’s assess Sushant's final position relative to his starting point:
  • North-South movement: He walked 5 km north, then another 5 km north, totaling 10 km north.
  • East-West movement: He walked 3 km west and then 3 km back east, which brings him back to the original east-west position he started from.
Given this analysis, Sushant's final destination is directly north of his house without any deviation east or west. Therefore, the correct answer is:
D: 10 km North

Mohan was facing east. he walked 4 km forward and then after turning to his right walked 3 km. Again he turned to his right and walked 4 km. After this he turned back. Which direction, was he facing at that time?
  • a)
    East
  • b)
    West
  • c)
    North
  • d)
    South
Correct answer is option 'A'. Can you explain this answer?

Kiran Reddy answered
According to given data let's make Mohan walking route direction;
Before turning back his face was in West direction.
After turned back his face should be in 'East' direction.
Hence, the correct answer is "East".

Two buses start from the opposite points of a main road, 150 km apart. The first bus runs for 25 km and takes a right turn and then runs for 15 km. It then turns left and runs for another 25 km and takes the direction back to reach the main road. In the meantime, due to a minor breakdown, the other bus has run only 35 km along the main road. What would be the distance between the two buses at this point ? 
  • a)
    65 km           
  • b)
    75 km
  • c)
    80 km           
  • d)
    85 km
Correct answer is option 'A'. Can you explain this answer?

Priyanka Menon answered
Given information:
- Two buses start from opposite points of a main road, 150 kms apart.
- The first bus runs for 25kms and takes a right turn and then runs for 15 kms.
- It then turns left and runs for another 25 kms and takes the direction back to reach the main road.
- The other bus has run only 35 kms along the main road.

To find:
- The distance between the two buses at this point.

Explanation:
Let's assume that the two buses meet at point X on the main road.

- The first bus travels a total distance of 25 + 15 + 25 = 65 kms before reaching point X.
- The second bus travels a total distance of 35 kms before reaching point X.
- Therefore, the distance between the two buses at point X is 150 - (65 + 35) = 50 kms.

Now, we need to find the distance between the two buses at the point where the first bus reaches the main road again.

- The first bus has covered a total distance of 2 * 25 + 15 = 65 kms from its starting point to reach the main road again.
- The second bus has covered a total distance of 35 + 25 = 60 kms from its starting point to reach the point where the first bus reached the main road again.
- Therefore, the distance between the two buses at this point is 150 - (65 + 60) = 25 kms.

Therefore, the distance between the two buses at the point where the first bus reaches the main road again is 25 kms.

Answer: Option A) 65 kms.

Shehnaz wants to go to the market. She started from her home which is in North and comes to a crossing. The road to her left ends in a park and straight ahead is the office complex. In which direction is the market from crossing?
  • a)
    East                   
  • b)
    West
  • c)
    North                          
  • d)
    South
Correct answer is option 'B'. Can you explain this answer?

Avantika Chakraborty answered
From the Fig, it is clear that Anoop starts his journey from point A and finishes his journey at point B. It can be seen that point B is at a distance of 10 m from point A and in the From the Fig, it is clear that Anoop starts his journey from point A and finishes his journey at point B. It can be seen that point B is at a distance of 10 m from point A and in the East direction.

Facing North, Ramesh walks 20 m, then he turns left and walks 30m, then again he turns left and walks 20 m. Then, he turns right and walks 10 m. How far is he now from his starting position?
  • a)
    30 m                           
  • b)
    25 m
  • c)
    40 m                           
  • d)
    45 m
Correct answer is option 'C'. Can you explain this answer?

Ishita Choudhury answered
To solve this problem, we need to visualize Ramesh's movements and calculate the distance between his final position and his starting position.

Let's break down Ramesh's movements step by step:

1. Ramesh walks 20 m facing North.
2. He turns left and walks 30 m.
3. He turns left again and walks 20 m.
4. He turns right and walks 10 m.

Calculating the North-South and East-West distances separately will help us determine the final position.

North-South Distance:
- Ramesh initially walks 20 m facing North.
- Then he turns left and walks 30 m, which means he moves 30 m towards the West.
- Finally, he turns left again and walks 20 m, which means he moves 20 m towards the South.

So, the total North-South distance covered by Ramesh is 20 m (North) - 20 m (South) = 0 m.

East-West Distance:
- Ramesh initially walks 20 m facing North.
- Then he turns left and walks 30 m, which means he moves 30 m towards the West.
- Finally, he turns left again and walks 20 m, which means he moves 20 m towards the South.
- After that, he turns right and walks 10 m, which means he moves 10 m towards the East.

So, the total East-West distance covered by Ramesh is 20 m (West) + 10 m (East) = 30 m.

Using the Pythagorean theorem, we can calculate the distance between Ramesh's final position and his starting position:

Distance = √((North-South Distance)^2 + (East-West Distance)^2)
= √((0 m)^2 + (30 m)^2)
= √(0 + 900)
= √900
= 30 m

Therefore, Ramesh is 30 m away from his starting position. The correct answer is option (a) 30 m.

X and Y started from a fixed point. X moves towards North and after walking 3 km turns to his right and covers 4 km. Y moves towards West and walks 5 km and then turns to his right and walks 3 km. How far X and Y are from each other?
  • a)
    5km                    
  • b)
    9km
  • c)
    6km                    
  • d)
    10km
Correct answer is option 'B'. Can you explain this answer?

Sahana Nair answered
To find out how far X and Y are from each other, we can plot their movements on a coordinate plane.

Let's assume the starting point as the origin (0,0). X moves towards the North, which means it moves along the positive y-axis. After walking 3 km, X turns to its right (clockwise) and covers 4 km. This means X moves 4 km along the positive x-axis. So, the final position of X is (4,3).

Y moves towards the West, which means it moves along the negative x-axis. After walking 5 km, Y turns to its right and covers 3 km. This means Y moves 3 km along the negative y-axis. So, the final position of Y is (-5,-3).

Using the distance formula, we can calculate the distance between the final positions of X and Y:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values:
Distance = √((4 - (-5))^2 + (3 - (-3))^2)
= √(9^2 + 6^2)
= √(81 + 36)
= √117
≈ 10.82

Rounding off to the nearest whole number, the distance between X and Y is approximately 11 km.

Therefore, the correct answer is option 'B' - 9 km.

Hemant started from his house and walked 3km eastward, then he turned right and walked 2km, then again he turned left and walked 1 km, then turned right and walked 2 km. He turned right again and walked 1 km and reached his school. What is the minimum distance between Hemant’s house and his school?
  • a)
    12 km                                                     
  • b)
    9km   
  • c)
    6 km                                                       
  • d)
    5 km   
Correct answer is option 'D'. Can you explain this answer?

Vertex Academy answered
To solve this, let's break down Hemant's movements step by step and visualize his path:
  1. Hemant starts from his house and walks 3 km eastward.
  2. He turns right and walks 2 km south.
  3. He turns left and walks 1 km east.
  4. He turns right and walks 2 km south.
  5. He turns right and walks 1 km west and reaches his school.
Now, let's consider the overall east-west and north-south movement:
  • East-West: Hemant initially walked 3 km east, then 1 km east, and finally 1 km west. So, the net eastward distance is 3 + 1 − 1 = 3 km.
  • North-South: Hemant walked 2 km south, then another 2 km south, so he walked a total of 2 + 2 = 4 km south.
The minimum distance from Hemant’s house to the school can be found using the Pythagorean theorem (since he moved in perpendicular directions):

Thus, the minimum distance between Hemant’s house and his school is: D: 5 km

A man is performing yoga with his head down and legs up. His face is towards the West. In which direction, will his left hand be?
  • a)
    North                          
  • b)
    South
  • c)
    East                   
  • d)
    West
Correct answer is option 'A'. Can you explain this answer?

Avantika Chakraborty answered
 If you face towards west your left hand will be pointing towards the south when held straight side ways horizontally, now the person is upside down so obviously the direction of the left hand will be opposite, so it will be facing north direction.

A starts from his house and moves towards B’s house which is 4km North.  After walking for three-fourth of the distance he finds B coming towards him along with C, who is A’s enemy. Wanting to avoid him, A takes a left turn and runs for a distance of 2kms.Now, if from this point (say ‘P’) he decides to go to B’s house, how much distance would he need to cover?
  • a)
    3km                                                        
  • b)
    Ö5km                                
  • c)
    1km                                                        
  • d)
    Ö3km                                
Correct answer is option 'B'. Can you explain this answer?

Vertex Academy answered
Let's analyze the path taken by A and the distances involved:
  1. A moves towards B's house: A starts moving north towards B's house which is 4 km away.
  2. A covers three-fourth of the distance: He covers 4 × 3/4 = 3 km towards the north.
  3. A takes a left turn: At this point, A is 1 km away from B's house (since he has covered 3 km out of 4 km). He then takes a left turn, which would be towards the west and runs 2 km.
Now, A is 1 km south of B's house and 2 km west of a direct line north from B’s house. To find the distance from point P (A's new location) to B's house, we use the Pythagorean theorem:

Thus, A would need to cover a distance of: B: √5km  

Namratha walks 14 metres towards west, then turns to her right and walks 14 meters and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance (in metres) between her starting point and her present position?  
  • a)
    38m
  • b)
    28m
  • c)
    24m
  • d)
    10m
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Hridoy Das answered
Let's break down Namratha's movements step by step:
  1. First Movement: She walks 14 meters west.
  2. Second Movement: She turns right and walks 14 meters north.
  3. Third Movement: She turns left and walks 10 meters west.
  4. Fourth Movement: She turns left again and walks 14 meters south.
Now, let's analyze her position.
  • After the first movement, she's 14 meters west of the starting point.
  • After the second movement, she's 14 meters west and 14 meters north of the starting point.
  • After the third movement, she's 24 meters west and 14 meters north of the starting point.
  • After the fourth movement, she moves 14 meters south, so she's now 24 meters west and at the same latitude as her starting point (because the south movement cancels out the north movement).
To find the shortest distance between her starting point and her present position, we just need to calculate the straight-line distance (which is the horizontal distance since her vertical displacement is zero).
Since she is 24 meters west of her starting point, the shortest distance is:
Distance=24 meters\text{Distance} = 24 \text{ meters}Distance=24 meters
So the correct answer is 24 meters (Option 3).
 

One morning after sunrise, Bikram and Shailash were standing in a town with their backs towards each other. Bikram’s shadow fell exactly towards left hand side. Which direction was Shailash facing?
  • a)
    East                    
  • b)
    West
  • c)
    North                            
  • d)
    South
Correct answer is option 'D'. Can you explain this answer?

Nandini Gupta answered
Sun rises in the East. It is given that "one morning after sunrise", therefore, we will mark Sun in the East direction in the below diagram.
When Sun is in the East direction, shadow of an object falls in the West. 
It is given that Bikram's shadow falls towards left hand side. This means Bikram's left hand side should be West direction.
In the question above pattern followed is,

Therefore the correct answer is Option D South.

Rohan walked 40 metres towards North, took a left turn and walked 20 metres. He again took a left turn and walked 40 metres. The distance and the direction in which he is from the starting point is
  • a)
    20 metres East
  • b)
    20 metres North
  • c)
    20 metres West
  • d)
    100 metres South
Correct answer is option 'C'. Can you explain this answer?

EduRev GATE answered
Given
1. Rohan walked 40 metres towards North, took a left turn and walked 20 metres.
2. He again took a left turn and walked 40 metres.
According to the given information, we get the following figure,

Therefore, above figure clearly shows the distance from B to A is 20 metres
The direction of B with respect to A is West.
Hence, "20 metres West" is the correct answer.

Sudha wants to go to the university and starts from her home which is in the East and comes to a crossing. The road to her left ends in a theatre. Straight ahead lies the hospital. In which direction is the university?
  • a)
    East                    
  • b)
    West
  • c)
    South             
  • d)
    North
Correct answer is option 'D'. Can you explain this answer?

Iq Funda answered
To determine the direction of the university from Sudha's starting point:
  • Sudha starts from her home, which is in the East.
  • At the crossing, the road to the left leads to a theatre.
  • Going straight ahead leads to a hospital.
  • Considering these directions, the university must be in the North.

Tanuj started walking from a point ‘P’ towards South. After walking 40 metres he took a left turn. He then walked 30 metres and reached a point Q.  What is the straight distance between P and Q and Q is towards in which direction with reference to point P?          
  • a)
    60 metres, South-East         
  • b)
    50 metres, South-West               
  • c)
    50 metres, South-East                   
  • d)
    Data Inadequate           
Correct answer is option 'C'. Can you explain this answer?

Pk Academy answered
Step 1: Tanuj starts from point P and walks 40 metres south.
Step 2: He takes a left turn (facing east) and walks 30 metres to reach point Q.
Applying the Pythagorean Theorem:
The path forms a right-angled triangle with:
One side = 40 metres (southward movement)
Another side = 30 metres (eastward movement)
Using the Pythagorean theorem to find the distance from P to Q:
PQ = √(40² + 30²) = √(1600 + 900) = √2500 = 50 metres
Direction of Q from P:
Since Tanuj moved south first and then east, Q is located South-East of P.
Answer:
c) 50 metres, South-East

Chapter doubts & questions for Distance & Direction - General Test Preparation for CUET UG 2025 is part of CUET Commerce exam preparation. The chapters have been prepared according to the CUET Commerce exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CUET Commerce 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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