Question 1

Ravi's house is to the west of Ankit's house, and Lavi's house is to the north of Ankit's house. In which direction is Lavi's house located with respect to Ravi's house?

Accepted Answer

Introduction / Context:This is a straightforward relative position problem involving three houses. Once we fix one house as a reference point, the positions of the other two can be represented on a simple grid. We then determine the direction of one house as seen from another by comparing their relative coordinates. Such problems are fundamental in direction sense topics and help in building a strong base for harder puzzles.Given Data / Assumptions:Ravi's house is to the west of Ankit's house.Lavi's house is to the north of Ankit's house.We are asked for the direction of Lavi's house relative to Ravi's house.All directions follow the standard compass with north up and east to the right.Concept / Approach:We place Ankit's house at the origin of a coordinate system for convenience. Since Ravi's house is to the west of Ankit's house, we place Ravi's house on the negative side of the x axis. Since Lavi's house is to the north of Ankit's house, we place Lavi's house on the positive side of the y axis. The relative direction of Lavi's house from Ravi's house is obtained by drawing a line from Ravi's coordinate to Lavi's coordinate and reading off the resulting quadrant, which in this case is north east.Step-by-Step Solution:Step 1: Place Ankit's house at the origin (0, 0) for reference.Step 2: Ravi's house is to the west of Ankit's house. So if we take one unit of distance for simplicity, Ravi's house could be at (-1, 0).Step 3: Lavi's house is to the north of Ankit's house. So Lavi's house could be at (0, 1).Step 4: From Ravi's point of view, we need the direction from (-1, 0) to (0, 1).Step 5: To go from (-1, 0) to (0, 1), we move one unit east (increasing x from -1 to 0) and one unit north (increasing y from 0 to 1).Step 6: A combined movement of north and east corresponds to the diagonal direction north east.Verification / Alternative check:Visualising on a compass, imagine Ankit's house at the centre. Ravi's house lies to the left (west) of this centre and Lavi's house lies above (north) of this centre. Connecting Ravi's point on the left to Lavi's point above forms a line that slopes upward to the right, which is the north east direction from Ravi to Lavi. This alignments confirms the coordinate based reasoning.Why Other Options Are Wrong:Option A (South-West) would be the reverse direction from Lavi to Ravi, not from Ravi to Lavi. Option C (North-West) would require Lavi's house to be farther west than Ravi's house, which is not the case. Option D (South-East) mixes the vertical direction incorrectly because we clearly move northward from Ravi to Lavi, not southward. Only option B correctly states that Lavi's house is to the north east of Ravi's house.Common Pitfalls:Students sometimes confuse the direction between two points with its reverse. It is important to carefully read which point is considered the reference. Another common issue is thinking in a relative way but forgetting that moving east from a western point and north from a southern point produces a north east resultant direction. Drawing a quick L shaped arrow from Ravi to Lavi usually settles the matter.Final Answer:With respect to Ravi's house, Lavi's house is located in the north east direction, so the correct option is “North-East”.

Question 2

Two cars C and D start from the same point. Car C first travels 9 km towards the south, then turns to its left and travels another 11 km. Car D first travels 3 km towards the east, then turns towards the south and travels 5 km, and finally turns to …

Accepted Answer

Introduction / Context:
In this direction sense test question, the movements of two cars are described using distances and turns. The task is to track both cars on an imaginary grid and then determine the relative position of car D with respect to car C. Such questions test spatial visualization, systematic plotting, and understanding of directions like north, south, east, and west.
Given Data / Assumptions:

C and D start from the same origin point.
Car C: 9 km south, then left turn, 11 km more.
Car D: 3 km east, then 5 km south, then left turn, 8 km.
Standard convention: north is up, south is down, east is right, west is left.

Concept / Approach:
We model movements on a coordinate plane. Take the starting point as (0, 0). Moving east increases the x coordinate, moving west decreases it, moving north increases the y coordinate, and moving south decreases it. After finding final coordinates of both cars, subtract the coordinates of C from those of D to find the relative displacement of D from C.
Step-by-Step Solution:
Set the starting point O as (0, 0).
Car C moves 9 km south: C1 = (0, -9).
From facing south, a left turn means facing east, so C moves 11 km east: C2 = (11, -9).
Car D moves 3 km east: D1 = (3, 0).
Then D moves 5 km south: D2 = (3, -5).
From facing south, a left turn means facing east, so D moves 8 km east: D3 = (11, -5).
Final coordinates: C at (11, -9) and D at (11, -5).
Relative position of D from C = (11 - 11, -5 - (-9)) = (0, 4).
This means D is 4 km directly north of C.
Verification / Alternative check:
Instead of coordinates, you can visualize the diagram. Both cars end up on the same vertical line (same east west level), but D has moved 4 km more towards the north than C. Therefore, D must be directly north of C, at a distance of 4 km.
Why Other Options Are Wrong:
Option A: 4 km South is opposite to the actual direction, because D is above C, not below. 
Option B: 14 km North exaggerates the distance; the northward gap is only 4 km. 
Option D: 14 km South is incorrect in both direction and distance. 
Option E: None of these is incorrect because one of the given options exactly matches the correct answer.
Common Pitfalls:
Students often confuse left and right turns when facing south, or mix up absolute and relative positions. Another frequent error is comparing each car with the origin instead of comparing D with C. Using systematic coordinates or a quick rough sketch helps prevent mistakes in such reasoning problems.
Final Answer:
Car D is located 4 km North of the final position of car C.

Question 3

A and B start from the same point. A cycles 8 km towards the south, then turns to her right and cycles 5 km. B cycles 3 km towards the north, then turns to the west and cycles 5 km, and finally turns to her left and cycles 4 km. After these movement…

Accepted Answer

Introduction / Context:
This problem is a classic direction sense test where two persons, A and B, start from the same point and travel in different directions with several turns. The aim is to determine the final relative position of B with respect to A by tracking their paths systematically on an imaginary grid. It checks careful reading of directions, understanding of right and left from the current facing, and displacement calculation.
Given Data / Assumptions:

A travels 8 km south from the common starting point.
Then A turns right from south and cycles 5 km west.
B travels 3 km north from the starting point.
Then B turns west and cycles 5 km.
Finally, B turns left from west and cycles 4 km south.
Standard north, south, east, west directions are used.

Concept / Approach:
We interpret movements on a coordinate plane. Choose the starting point as (0, 0). For south decrease the y coordinate, for north increase it; for east increase the x coordinate, and for west decrease it. After computing the final coordinates of A and B, we subtract A position from B position to find the relative displacement of B from A and convert this into a direction and distance statement.
Step-by-Step Solution:
Let the start point be O = (0, 0).
A moves 8 km south: A1 = (0, -8).
Facing south, a right turn leads to west, so A moves 5 km west: A2 = (-5, -8).
B moves 3 km north: B1 = (0, 3).
Then B turns west and moves 5 km: B2 = (-5, 3).
Facing west, a left turn points south, so B moves 4 km south: B3 = (-5, -1).
Final positions: A at (-5, -8) and B at (-5, -1).
Relative position of B from A = (-5 + 5, -1 + 8) = (0, 7).
So B is 7 km due north of A.
Verification / Alternative check:
Draw a simple grid. Both paths end on the same vertical line (same west displacement), but B is clearly higher than A by 7 km. This confirms that B is directly north of A at a distance of 7 km, matching our coordinate calculation.
Why Other Options Are Wrong:
Option B: 7 km South reverses the direction. 
Option C and Option D: 15 km North or South exaggerate the distance and are not supported by the movement data. 
Option E: None of these is incorrect because we have an exact match in Option A.
Common Pitfalls:
A common mistake is to forget that left and right depend on the current facing direction, not on the page. Another pitfall is mixing up absolute positions with relative positions and comparing each person only to the origin instead of directly comparing A and B positions. Using coordinates or a rough diagram greatly reduces errors.
Final Answer:
B is located 7 km North of the final position of A.

Question 4

X and Y both start from the same point. X walks 17 metres towards the west and then turns to his right and walks 13 metres. At the same time, Y walks 9 metres towards the north, then turns to the east and walks 7 metres, and finally turns to his lef…

Accepted Answer

Introduction / Context:
This direction sense question describes two different paths starting from the same origin for persons X and Y. The objective is not to find their distances from the starting point, but to find where Y stands relative to X after both complete their movements. Such questions are standard in reasoning tests and rely on a systematic breakdown of movements into north, south, east, and west components.
Given Data / Assumptions:

Both X and Y start from the same point.
X walks 17 m west, then turns right and walks 13 m north.
Y walks 9 m north, then 7 m east, then turns left and walks 4 m north.
All turns are right angle turns.
We follow the usual convention for directions on a coordinate grid.

Concept / Approach:
We represent the motion on a coordinate plane. The starting point is taken as (0, 0). Moving west reduces the x coordinate, while moving east increases it. Moving north increases the y coordinate, while moving south reduces it. After calculating the final coordinates of X and Y, we subtract the coordinates of X from those of Y to identify the relative position of Y with respect to X.
Step-by-Step Solution:
Start at O = (0, 0).
X walks 17 m west: X1 = (-17, 0).
From facing west, a right turn leads north, so X walks 13 m north: X2 = (-17, 13).
Y walks 9 m north: Y1 = (0, 9).
Then Y walks 7 m east: Y2 = (7, 9).
Facing east, a left turn leads north, so Y walks 4 m north: Y3 = (7, 13).
Final positions: X at (-17, 13) and Y at (7, 13).
Relative position of Y from X = (7 - (-17), 13 - 13) = (24, 0).
Therefore, Y is 24 m due east of X.
Verification / Alternative check:
On a rough sketch, both X and Y end at the same north level (same y coordinate), but Y is much further to the right. Counting horizontal separation from x = -17 to x = 7 gives 24 m, confirming the calculation.
Why Other Options Are Wrong:
Option A and Option C state west instead of east, which contradicts the final layout. 
Option B: 10 m East is too small; the correct separation is 24 m. 
Option E: None of these is not correct because one of the given choices, 24 m East, is exactly right.
Common Pitfalls:
Learners might forget to track directions after each turn or might mix up right and left when facing west or east. Another pitfall is comparing only one person to the origin instead of taking the difference between positions. Building a simple x y table or a clear sketch helps avoid these mistakes.
Final Answer:
Y is located 24 m East of the final position of X.

Question 5

A marketing executive goes on his field work and first walks 2 km towards the north, then turns towards the west and walks 6 km. After that he again turns towards the north and walks 7 km, and finally turns to his right and walks 6 km. Where is he n…

Accepted Answer

Introduction / Context:
This question describes the trip of a marketing executive who makes several turns while walking fixed distances in different directions. The goal is to determine his final position relative to his starting point. Direction sense problems of this type are common in verbal reasoning and test the ability to translate word descriptions into a mental or drawn map and then compute net displacement.
Given Data / Assumptions:

He starts from a point we call the origin.
First he walks 2 km north.
Then he turns west and walks 6 km.
Next he turns north and walks 7 km.
Finally he turns to his right from facing north and walks 6 km east.
We use the standard orientation of north, south, east, and west on a coordinate grid.

Concept / Approach:
We treat the movements as vectors on a coordinate plane. Let the starting point be (0, 0). Moving north increases the y coordinate, moving south decreases it, moving east increases the x coordinate, and moving west decreases it. By adding each movement step by step, we obtain the final coordinates and then interpret the net displacement as a distance and direction from the origin.
Step-by-Step Solution:
Take the starting point as (0, 0).
Walking 2 km north leads to position (0, 2).
Turning west and walking 6 km leads to position (-6, 2).
Turning north and walking 7 km leads to position (-6, 9).
From facing north, a right turn means facing east; walking 6 km east leads to position (0, 9).
Final coordinates relative to the origin: (0, 9).
Thus, the executive is 9 km directly north of his starting point.
Verification / Alternative check:
We can also reason verbally. The 6 km west and 6 km east movements cancel each other out, leaving no net east west displacement. The north movements are 2 km and 7 km, for a total of 9 km north, with no southward movement to cancel them. Hence he must be 9 km north of his starting position.
Why Other Options Are Wrong:
Option A: 5 km North underestimates the total northward displacement. 
Options C and D mention south, which is opposite to the actual direction. 
Option E: None of these is incorrect because 9 km North is explicitly available in the options as the correct answer.
Common Pitfalls:
Common mistakes include misinterpreting a right turn from north as west instead of east, or failing to notice that opposite horizontal displacements cancel out. Another frequent issue is to add distances without regard to direction. Carefully tracking net north south and east west movements avoids these errors.
Final Answer:
The marketing executive is 9 km North of his starting position.

Question 6

Pranav first goes 10 km towards the north. Then he turns towards the west and covers 10 km. After that he turns towards the south and covers 5 km, and finally he turns towards the east and covers 10 km. In which direction is he now from his original…

Accepted Answer

Introduction / Context:
This direction sense problem describes a path that resembles a rectangular route with unequal sides. The aim is to track Pranav position after moving north, west, south, and then east. Instead of only visualizing the path, we must compute the net displacement and then express the final direction from the starting point. Problems of this type are frequently used to test basic spatial reasoning and understanding of cardinal directions.
Given Data / Assumptions:

Pranav starts from an origin point.
He walks 10 km north.
He then walks 10 km west.
He then walks 5 km south.
Finally, he walks 10 km east.
All distances are in kilometres and all turns represent right angle changes of direction.

Concept / Approach:
We can regard his motions as vectors on a coordinate plane. Let the starting point be at (0, 0). Movements towards north add to the y coordinate, movements towards south subtract from y, movements towards east add to the x coordinate, and movements towards west subtract from x. After summing all movements, we interpret the final coordinate pair as a displacement from the origin and convert that into a simple directional statement.
Step-by-Step Solution:
Start at (0, 0).
Move 10 km north to reach (0, 10).
Move 10 km west to reach (-10, 10).
Move 5 km south to reach (-10, 5).
Move 10 km east to reach (0, 5).
Final position relative to origin is (0, 5).
This means Pranav is 5 km directly north of his starting point.
Verification / Alternative check:
Horizontally, Pranav goes 10 km west and then 10 km east, which cancel each other, leaving no net east west displacement. Vertically, he goes 10 km north and then 5 km south, so he remains 5 km to the north of the origin. Therefore his final direction from the starting point is simply north.
Why Other Options Are Wrong:
Option A: South is opposite to the actual net vertical movement. 
Option C and Option D: East and West are incorrect because the net horizontal displacement is zero. 
Option E: None of these is wrong because North is already present as a correct option.
Common Pitfalls:
Many learners erroneously assume that returning to the east after going west always brings them back to the same vertical line, which is correct, but then mistakenly conclude that the entire path forms a closed loop. Another pitfall is ignoring that the southward distance is less than the northward distance, which leaves a remaining northward displacement. Carefully comparing totals in each direction avoids these mistakes.
Final Answer:
Pranav is finally walking in the North direction from his starting point.

Question 7

A car travels 17 km towards the south, then turns towards the east and travels 11 km. After that it turns towards the north and travels 9 km, and finally it turns to its left and travels another 11 km. Where is the car now with reference to its orig…

Accepted Answer

Introduction / Context:
This direction sense problem involves a car making several movements and turns, ultimately forming a path that partially cancels out. The question asks for the final position of the car relative to where it started, in terms of direction and distance. It tests understanding of cardinal directions, turning left while facing a given direction, and net displacement calculation.
Given Data / Assumptions:

The car starts from an origin point.
First it travels 17 km south.
Then it turns east and travels 11 km.
Next it turns north and travels 9 km.
Finally, from facing north, it turns left and travels 11 km west.
All movements are in straight lines with right angle turns.

Concept / Approach:
We model all movements as vectors on an x y coordinate plane. Taking the starting point as (0, 0), south decreases the y coordinate, north increases it, east increases the x coordinate, and west decreases it. After each movement, we update the coordinates and then inspect the final coordinates to determine both the direction and magnitude of displacement from the starting point.
Step-by-Step Solution:
Take the starting position as (0, 0).
Travelling 17 km south gives (0, -17).
Turning east and travelling 11 km gives (11, -17).
Turning north and travelling 9 km gives (11, -8).
From facing north, a left turn means west, so travelling 11 km west gives (0, -8).
Final position relative to the origin is (0, -8).
Thus, the car is 8 km south of its starting point.
Verification / Alternative check:
Observe that the 11 km east and 11 km west cancel each other, leaving no net horizontal displacement. For vertical movement, the car goes 17 km south and only 9 km north, so net displacement is 17 - 9 = 8 km towards the south. This independent argument confirms the coordinate based solution.
Why Other Options Are Wrong:
Option A: 8 km North reverses the actual net direction. 
Option C and Option D: 26 km South or 26 km North misrepresent both direction and magnitude. 
Option E: None of these is not correct because 8 km South appears explicitly and matches the correct result.
Common Pitfalls:
Some learners confuse the final left turn from north, incorrectly assuming it leads east instead of west. Others simply add distances without considering cancellations between opposite directions. The key is to separate horizontal and vertical components and compute net movement in each axis carefully.
Final Answer:
The car is finally located 8 km South of its starting position.

Question 8

A man walks 5 km towards the south and then turns to his right. After walking 3 km, he turns to his left and walks a further 5 km. After completing this route, in which direction is he located from his original starting point?

Accepted Answer

Introduction / Context:
This is a direction sense question where a man walks along three line segments with specified turns. The focus is on interpreting right and left turns correctly based on current orientation and then determining the final direction of the man from his starting point. Such questions are common in exams to test mental mapping skills and careful interpretation of directions.
Given Data / Assumptions:

He starts from an origin point.
He walks 5 km south.
From facing south, he turns right and walks 3 km west.
From facing west, he turns left and walks 5 km south.
We only need the final direction from the starting point, not the exact distance.

Concept / Approach:
We treat movements on a coordinate plane. The starting point is (0, 0). Movement towards the south decreases the y coordinate, movement towards the north increases it, movement towards the east increases the x coordinate, and movement towards the west decreases it. After computing the final coordinates, we look at the signs and magnitudes of x and y to identify the quadrant and hence the direction (for example, south west if x is negative and y is negative).
Step-by-Step Solution:
Start at (0, 0).
Walk 5 km south to reach (0, -5).
Facing south, a right turn leads west, so walk 3 km west to reach (-3, -5).
Facing west, a left turn leads south, so walk another 5 km south to reach (-3, -10).
Final position relative to origin is (-3, -10).
Negative x means west of origin and negative y means south of origin, so he is in the south west direction from the starting point.
Verification / Alternative check:
Visualizing on a diagram, he first goes down, then left, then further down. The final point lies below and to the left of the start. Since we are only asked for direction, not distance, it is sufficient to note it is both south and west, that is, south west.
Why Other Options Are Wrong:
Option A: West would ignore the strong southward displacement. 
Option B: South would ignore the westward displacement. 
Option C: North East is in the opposite quadrant and clearly incorrect. 
Option E: None of these is incorrect because South West is explicitly given.
Common Pitfalls:
Candidates sometimes misapply right and left turns when facing south or west, imagining them relative to the page rather than to the walker orientation. Another error is assuming that only the last direction of movement matters, instead of assessing the net displacement. Always track cumulative x and y changes for reliability.
Final Answer:
The man is finally located in the South-West direction from his starting point.

Question 9

Deepu starts his journey from point A and moves 2 km towards the south. Then he turns to his right and moves 0.5 km. Again he takes a right turn and walks 2 km. Now he takes a left turn and walks 3 km more. How far is he from his starting point A af…

Accepted Answer

Introduction / Context:
In this direction sense and distance problem, Deepu travels in four legs with right and left turns, some of which have fractional distances. The question asks for his straight line distance from the starting point, not the total path length. It combines understanding of turns with basic coordinate geometry and Pythagoras theorem for distance.
Given Data / Assumptions:

Deepu starts from point A.
He walks 2 km south.
He then turns right from facing south and walks 0.5 km west.
He again turns right from facing west and walks 2 km north.
He finally turns left from facing north and walks 3 km west.
We need the shortest straight line distance from his final position to point A.

Concept / Approach:
We plot the movement on a coordinate plane. Let A be at (0, 0). South reduces the y coordinate, north increases it, east increases the x coordinate, and west reduces it. After computing final coordinates, we compute the straight line distance from the origin using the distance formula derived from Pythagoras theorem: distance = sqrt(x^2 + y^2).
Step-by-Step Solution:
Start at A = (0, 0).
Move 2 km south: position becomes (0, -2).
Facing south, a right turn leads west, so move 0.5 km west: position becomes (-0.5, -2).
Facing west, a right turn leads north, so move 2 km north: position becomes (-0.5, 0).
Facing north, a left turn leads west, so move 3 km west: position becomes (-3.5, 0).
Final coordinates relative to A are (-3.5, 0).
Distance from A = sqrt((-3.5)^2 + 0^2) = 3.5 km.
Verification / Alternative check:
Visually, his vertical movement is 2 km down and 2 km up, cancelling out completely, so he ends on the same east west line as A. Horizontally, he goes 0.5 km west and then 3 km further west, for a total of 3.5 km west of A. Since there is no vertical separation, the straight line distance equals this horizontal distance, 3.5 km.
Why Other Options Are Wrong:
Option B: 2.5 km is less than the total westward displacement. 
Option C: 7.5 km is far too large and confuses path length with net displacement. 
Option D: 1.5 km underestimates the actual separation. 
Option E: None of these is wrong because one of the given values, 3.5 km, exactly matches the computation.
Common Pitfalls:
Students sometimes forget that opposite vertical movements cancel or treat the 0.5 km segment as 5 km due to misreading. Another common mistake is to add all distances to estimate displacement, which is incorrect when path turns are involved. Always separate horizontal and vertical components and then apply the distance formula.
Final Answer:
Deepu is 3.5 km away from his starting point A.

Question 10

Prem starts from his house and walks 400 metres towards the north. Then he turns left and walks 100 metres. Next he turns left again and walks 200 metres. Finally he turns left once more and walks 100 metres. After completing this path, how far is h…

Accepted Answer

Introduction / Context:
This problem describes a path taken by Prem with several left turns and asks for his final distance from his starting point, his house. The motion forms a simple shape that can be represented on a coordinate plane. It tests basic understanding of direction changes, along with the idea that some movements may partially cancel out when they occur in opposite directions.
Given Data / Assumptions:

Prem starts from his house at an origin point.
He walks 400 m north.
He turns left from facing north and walks 100 m west.
He again turns left from facing west and walks 200 m south.
He turns left once more from facing south and walks 100 m east.
We only need the straight line distance from his final position back to his house.

Concept / Approach:
We use a coordinate grid for clarity. Let the house be at (0, 0). Movements north increase the y coordinate, movements south decrease it, movements east increase the x coordinate, and movements west decrease it. After tracking all movements, we examine the final coordinates and compute displacement using the distance formula if needed. In this particular case, all horizontal movements cancel exactly, making the calculation especially simple.
Step-by-Step Solution:
Set the starting point at (0, 0).
Walk 400 m north to reach (0, 400).
Facing north, a left turn leads west, so walk 100 m west to reach (-100, 400).
Facing west, a left turn leads south, so walk 200 m south to reach (-100, 200).
Facing south, a left turn leads east, so walk 100 m east to reach (0, 200).
Final coordinates are (0, 200).
Distance from the house is sqrt(0^2 + 200^2) = 200 m.
Verification / Alternative check:
Horizontally, Prem goes 100 m west and then 100 m east, which cancel. Vertically, he first goes 400 m north and then 200 m south, leaving a net 200 m north. Since he is directly north of his house with no east west separation, his straight line distance from home is simply 200 m.
Why Other Options Are Wrong:
Option A: 100 m only accounts for part of the net vertical displacement. 
Option B: 300 m exaggerates the remaining northward distance. 
Option D: 250 m is not supported by the component calculations. 
Option E: None of these is wrong because 200 m is present as a correct choice.
Common Pitfalls:
Students sometimes treat the entire path length as the displacement or forget that the last two horizontal legs cancel. Another pitfall is misinterpreting repeated left turns and drawing the path incorrectly. Keeping a clear sketch or systematic x y record prevents these errors.
Final Answer:
Prem is 200 m away from his house after the described movements.

Question 11

Two planes start from the same airport. Plane A flies 50 km towards the east. Plane B flies 15 km towards the north, then turns towards the east and flies 20 km, and then turns to its right and flies 15 km. After these movements, where is plane B lo…

Accepted Answer

Introduction / Context:
This direction sense question involves relative positions of two planes, each following different routes from the same airport. Rather than asking for each plane absolute distance from the airport, the problem focuses on the position of plane B relative to plane A. Solving this requires tracking movements on a coordinate plane and then comparing the final coordinates of the two planes.
Given Data / Assumptions:

Both planes start from the same airport.
Plane A flies 50 km east.
Plane B flies 15 km north.
Then B flies 20 km east.
Then B turns right from facing east and flies 15 km south.
The directions follow the standard compass orientation.

Concept / Approach:
We represent all positions in an x y coordinate system. Let the airport be at (0, 0). Flying east increases the x coordinate, flying west decreases it, flying north increases the y coordinate, and flying south decreases it. After calculating plane A and plane B final coordinates, we subtract A coordinates from B coordinates to find B displacement relative to A, and then express that result as a direction and distance.
Step-by-Step Solution:
Set the airport at (0, 0).
Plane A flies 50 km east to reach (50, 0).
Plane B flies 15 km north to reach (0, 15).
Then B flies 20 km east to reach (20, 15).
Facing east, a right turn leads south, so B flies 15 km south to reach (20, 0).
Final positions: A at (50, 0) and B at (20, 0).
Relative position of B from A = (20 - 50, 0 - 0) = (-30, 0).
Therefore, B is 30 km west of A.
Verification / Alternative check:
Observe that both planes end on the same east west line (same y coordinate). From the airport, A is 50 km east, while B, after going north and then south by equal amounts, ends directly east of the airport by only 20 km. Hence, from A perspective, B lies 30 km back towards the west, confirming our coordinate calculation.
Why Other Options Are Wrong:
Option A: 30 km East reverses the direction relative to A. 
Option B and Option D: 70 km East or West are not supported by any realistic difference based on the routes. 
Option E: None of these is incorrect because 30 km West is a correct option and matches the calculated displacement.
Common Pitfalls:
A typical mistake is to compare each plane only with the airport and then misread the relative offset, or to forget that the 15 km north and 15 km south legs of B cancel vertically. Another common error is reversing the direction when computing B relative to A. Carefully subtracting coordinates in the correct order avoids such confusion.
Final Answer:
Plane B is located 30 km West of plane A.

Question 12

P and Q start cycling from the same point. P cycles 18 km towards the north and then turns to her right and cycles 3 km. Q cycles 9 km towards the east, then turns towards the north and cycles 10 km, and finally turns left and cycles 6 km. Where is …

Accepted Answer

Introduction / Context:
In this direction sense test, two cyclists P and Q travel along different routes after starting from the same point. The question asks for the location of Q relative to P after both have completed their journeys. This type of problem checks careful tracking of directions, relative displacement, and the ability to convert movements into coordinates.
Given Data / Assumptions:

P cycles 18 km north from the starting point.
Then P turns right from facing north and cycles 3 km east.
Q cycles 9 km east from the starting point.
Then Q turns north and cycles 10 km.
Finally, Q turns left from facing north and cycles 6 km west.
We need the displacement of Q with respect to P.

Concept / Approach:
We use a coordinate geometry approach. Take the common starting point as (0, 0). North increases y, south decreases y, east increases x, and west decreases x. After computing the coordinates of P and Q final positions, we subtract P coordinates from Q coordinates to find the relative position of Q with respect to P and then express it as a direction and distance.
Step-by-Step Solution:
Start at (0, 0).
P cycles 18 km north to reach (0, 18).
Facing north, a right turn leads east, so P cycles 3 km east to reach (3, 18).
Q cycles 9 km east to reach (9, 0).
Then Q cycles 10 km north to reach (9, 10).
Facing north, Q turns left and cycles 6 km west to reach (3, 10).
Final positions: P at (3, 18) and Q at (3, 10).
Relative position of Q from P = (3 - 3, 10 - 18) = (0, -8).
Thus, Q is 8 km south of P.
Verification / Alternative check:
Notice both P and Q end on the same vertical line x = 3, so there is no east west separation between them. For vertical displacement, P is at y = 18 while Q is at y = 10. Hence, Q is 8 km downwards from P, that is, in the south direction relative to P. This confirms our calculation.
Why Other Options Are Wrong:
Option B: 8 km North reverses the actual relative direction. 
Options C and D: 28 km South or 28 km North substantially overstate the distance and are inconsistent with the path lengths given. 
Option E: None of these is incorrect because one of the options, 8 km South, exactly matches the correct result.
Common Pitfalls:
It is easy to forget that the question asks for Q position with respect to P, not the airport or the origin. Another pitfall is misinterpreting the left turn from north as east instead of west. A simple coordinate diagram keeps the relative orientation clear and helps prevent such mistakes.
Final Answer:
Q is located 8 km South of the final position of P.

Question 13

To attend an examination, Sudhir reaches the school by travelling 5 km towards the south and then, after a sharp left turn, he travels 10 km. He again makes a sharp left turn and reaches in front of the school by travelling another 5 km. In which di…

Accepted Answer

Introduction / Context:
This question describes Sudhir journey to his school with two sharp left turns and asks for the direction of his starting point relative to the school. Rather than tracing the entire route backwards, we can plot the path on a coordinate plane, find the coordinates of the school, and then look back from the school towards the starting point to determine the appropriate direction.
Given Data / Assumptions:

Sudhir starts from a point that we take as the origin.
He travels 5 km south.
He then makes a sharp left turn from facing south and travels 10 km east.
He again makes a sharp left turn from facing east and travels 5 km north to reach the school.
We need the direction of the starting point as viewed from the school.

Concept / Approach:
We again use the coordinate plane method. Let the starting point be (0, 0). Moving south reduces the y coordinate, moving north increases it, moving east increases x, and moving west decreases x. After finding the coordinates of the school, we compute the vector from the school back to the starting point. The sign of the x and y components in that vector tells us the correct direction.
Step-by-Step Solution:
Take the starting point S as (0, 0).
Sudhir walks 5 km south to reach (0, -5).
Facing south, a sharp left turn leads east, so he travels 10 km east to reach (10, -5).
Facing east, another sharp left turn leads north, so he travels 5 km north to reach (10, 0). This point is the school.
Coordinates: starting point at (0, 0) and school at (10, 0).
Vector from school to starting point = (0 - 10, 0 - 0) = (-10, 0).
A negative x component indicates that the starting point lies to the west of the school.
Verification / Alternative check:
Conceptually, Sudhir goes straight down, then right, then up and ends horizontally displaced from his start. The south and north movements cancel exactly, so the school lies directly east of his starting point. Therefore, when viewed from the school, the starting point is directly to the west.
Why Other Options Are Wrong:
Option A: East is the position of the school relative to the starting point, not the other way round. 
Option C: North does not match any vertical displacement between the school and starting point. 
Option D: South is also incorrect because both points are at the same north south level. 
Option E: None of these is wrong because West is explicitly given and correct.
Common Pitfalls:
Many students confuse direction from A to B with direction from B to A. Another frequent error is forgetting that equal south and north distances cancel each other out, leaving only horizontal displacement. Always pay attention to whether the question asks for position of the destination from the source or the source from the destination.
Final Answer:
Sudhir starting point is to the West of the school.

Question 14

A man starts from a point, walks 5 km towards the east, then turns right and walks 3 km, and then turns right again and continues walking. What is the direction in which he is finally walking?

Accepted Answer

Introduction / Context:
This is a pure direction question that focuses only on the final facing direction of the man after a series of right angle turns. Unlike other problems, the exact distances do not affect the orientation. It is a quick test of understanding how successive right turns change a person facing east or south into a different final direction.
Given Data / Assumptions:

The man initially walks 5 km towards the east.
From facing east, he turns right and walks 3 km towards the south.
He then turns right again and continues walking, now heading towards the west.
The problem only asks for his final direction, not his position.

Concept / Approach:
When solving such questions, it is often enough to track orientation only. Starting from east, a right turn leads to south, and another right turn leads to west. Distance values do not change the direction in which the person is facing after the turns, so they can be ignored when determining orientation. Keeping a mental compass rose is very helpful.
Step-by-Step Solution:
Initial direction: east.
From east, a right turn leads to south.
So after the first turn, he is facing south while walking 3 km.
From south, another right turn leads to west.
Therefore, after the second right turn, he is facing west and continues in that direction.
Verification / Alternative check:
You can imagine a simple compass: starting from east, rotate clockwise by 90 degrees to reach south. Rotate again clockwise by another 90 degrees to reach west. This confirms that two successive right turns from an initial eastward direction end up pointing west. Drawing a simple diagram with arrows can also provide a quick visual check.
Why Other Options Are Wrong:
Option A: North would require three right turns from east or a left turn from west, which does not match the description. 
Option B: South is the direction after the first right turn, not after the second. 
Option D: South west is a diagonal direction, but all moves in this problem are strictly along cardinal directions, so it cannot be correct. 
Option E: None of these is wrong because West is clearly the correct final direction and appears as one of the options.
Common Pitfalls:
A typical mistake is to overthink the effect of distances or to imagine turns with respect to the page rather than to the person orientation. Another error is stopping after the first right turn instead of considering both. Always count turns carefully and use a consistent mental or drawn compass.
Final Answer:
The man is finally walking towards the West.

Question 15

P, Q, R, S and T are sitting in a straight line facing north. R is sitting at the extreme left end near the entrance. Q sits next to R. P sits next to S but not next to T. If T does not sit next to Q, then who sits to the immediate left of S?

Accepted Answer

Introduction / Context:
This is a linear seating arrangement question involving five persons P, Q, R, S and T seated in a straight line facing north. Several relational clues are provided regarding who sits next to whom and where R is located. The task is to use these constraints systematically to determine the unique seating order and then answer who sits to the immediate left of S.
Given Data / Assumptions:

All five persons sit in a straight line facing north.
R sits on the entrance left corner, that is, at the extreme left end.
Q sits next to R.
P sits next to S but not next to T.
T does not sit next to Q.
Left and right are considered from the view of someone facing north.

Concept / Approach:
We treat the five positions from left to right as positions 1 to 5. Since R is at the extreme left end, R must be in position 1. Because Q sits next to R, Q must be in position 2. T cannot sit next to Q, so T cannot be in position 3. We then place P and S so that they sit adjacent to each other and P is not adjacent to T. After all constraints are satisfied, we inspect who is directly to the left of S.
Step-by-Step Solution:
Place R at position 1 (extreme left).
Q must sit next to R, so place Q at position 2.
T cannot sit next to Q, so T cannot occupy position 3.
The remaining positions 3, 4, and 5 must be filled by P, S, and T.
P must sit next to S, so they must occupy adjacent positions among 3, 4, and 5.
If T were at 4, then P and S would be at 3 and 5, not adjacent, which is impossible.
Hence T must be at position 5.
Then P and S must occupy positions 3 and 4, in some order, and P must not sit next to T. Therefore T at 5 means position 4 cannot be P, so P must be at 3 and S at 4.
Final order from left to right: R, Q, P, S, T.
Thus, the person sitting to the immediate left of S is P.
Verification / Alternative check:
Check all constraints: R is at the left corner (position 1), Q sits next to R (position 2), T is not next to Q (T at 5), and P sits next to S (positions 3 and 4) but is not next to T (since T at 5 and P at 3 are separated by S). All conditions are satisfied, confirming the seating order and hence the answer.
Why Other Options Are Wrong:
Option B: Q sits to the left of P, not to the left of S. 
Option C: R is two seats away from S and not immediately to the left. 
Option D: T sits to the right of S, not to the left. 
Option E: None of these is incorrect because P is present in the list and is correct.
Common Pitfalls:
Some learners misinterpret left and right when everyone is facing north or forget the T not next to Q condition. Others try to guess the arrangement instead of systematically checking all possibilities. Writing out the positions and carefully applying each constraint in order is the most reliable method for such problems.
Final Answer:
The person sitting immediately to the left of S is P.

Question 16

A boy runs 20 metres towards the east and then turns to his right, runs 10 metres, and again turns to his right and runs 9 metres. He then turns left and runs 5 metres, turns left again and runs 12 metres, and finally turns left once more and runs 6…

Accepted Answer

Introduction / Context:
This problem describes a series of movements and multiple direction changes for a boy and asks only for the final direction he is facing, not his position. Direction sense questions of this type require careful tracking of each turn relative to the current facing, especially when there are several consecutive right and left turns.
Given Data / Assumptions:

Initial direction: the boy runs 20 m east.
He turns right and runs 10 m (towards the south).
He turns right again and runs 9 m (towards the west).
He turns left and runs 5 m (towards the south).
He turns left again and runs 12 m (towards the east).
He turns left once more and runs 6 m (towards the north).
We must determine only his final facing direction.

Concept / Approach:
It is often easier to track only orientation changes for such questions. Starting from east, a right turn leads to south, from south a right turn leads to west, from west a left turn leads to south, from south a left turn leads to east, and from east a left turn leads to north. Distances do not change orientation; only the sequence of left and right turns does. Keeping a mental or drawn compass helps avoid confusion.
Step-by-Step Solution:
Initial facing: east.
First turn: right from east gives south.
Second turn: right from south gives west.
Third turn: left from west gives south.
Fourth turn: left from south gives east.
Fifth turn: left from east gives north.
So, after all movements, the boy is facing north.
Verification / Alternative check:
Another way is to list directions as E, S, W, N around a circle in clockwise order. A right turn moves one step clockwise, and a left turn moves one step anticlockwise. Starting at E: right to S, right to W, left back to S, left to E, and left to N. Both methods confirm that the final facing direction is north.
Why Other Options Are Wrong:
Option A: East is only the initial direction and temporarily revisited before the last turn. 
Option B: West is the direction after the second turn, not final. 
Option D: South is the direction after the first and third turns, not after the entire sequence. 
Option E: None of these is incorrect because North is present and correct.
Common Pitfalls:
Learners often try to track both position and direction at the same time and become confused by distances, which do not matter for orientation. Another common issue is miscounting the number of turns or reversing left and right when facing south or west. Focusing purely on the sequence of turns and using a compass diagram prevents these errors.
Final Answer:
The boy is finally facing towards the North.

Question 17

Rahul walks 30 metres towards the south. Then he turns to his right and walks straight for another 30 metres. Next he turns to his left and walks 20 metres, and then turns to his left again and walks 30 metres. After completing this route, how far i…

Accepted Answer

Introduction / Context:
This direction and distance problem describes Rahul moving along four line segments with right and left turns. The task is to determine his straight line distance from his starting position after finishing the entire path. This requires translating the path into horizontal and vertical components and then using the distance formula to compute the net displacement.
Given Data / Assumptions:

Rahul walks 30 m south from his initial position.
He then turns right from facing south and walks 30 m west.
He then turns left from facing west and walks 20 m south.
He finally turns left from facing south and walks 30 m east.
Distances are in metres and all turns are right angles.

Concept / Approach:
We use a coordinate plane. Let the starting point be (0, 0). South decreases the y coordinate, north increases it, east increases x, and west decreases x. Once we determine the final coordinates, the straight line distance from the origin is obtained using the formula distance = sqrt(x^2 + y^2). Observing cancellations between opposite directions can also simplify reasoning.
Step-by-Step Solution:
Start at (0, 0).
Walk 30 m south to reach (0, -30).
Facing south, a right turn leads west; walk 30 m west to reach (-30, -30).
Facing west, a left turn leads south; walk 20 m south to reach (-30, -50).
Facing south, a left turn leads east; walk 30 m east to reach (0, -50).
Final coordinates are (0, -50), meaning Rahul is 50 m south of his starting point.
Straight line distance from start = sqrt(0^2 + 50^2) = 50 m.
Verification / Alternative check:
Horizontally, Rahul moves 30 m west and 30 m east, which cancel out completely. Vertically, he first moves 30 m south, then an additional 20 m south, for a total of 50 m south. With no horizontal displacement remaining, his straight line distance from the start is exactly his southward displacement, 50 m.
Why Other Options Are Wrong:
Option B: 30 m only accounts for part of the southward movement. 
Option C: 10 m is far too small and ignores the overall path. 
Option D: 60 m exceeds the total southward movement and is not supported by the net displacement. 
Option E: None of these is incorrect because 50 metres is explicitly listed and correctly matches the analysis.
Common Pitfalls:
Students sometimes add all segment lengths to estimate displacement or confuse intermediate positions with the final location. Another pitfall is misinterpreting left turns from non north orientations. A small grid sketch or a table of x y values for each step is an efficient defence against these mistakes.
Final Answer:
Rahul is 50 metres away from his initial position.

Question 18

Sanmitra walks 8 metres towards the north. He then turns to his right and walks 16 metres, turns to his left and walks 5 metres, and again turns to his left and walks 16 metres. In which direction is he now from his starting point?

Accepted Answer

Introduction / Context:
This direction sense problem describes a walk with several turns forming a rectangular path. We are asked to determine the final direction of Sanmitra from his starting point. Rather than requiring the exact distance, the question focuses only on the relative orientation, which can often be answered by carefully comparing total north south and east west movements.
Given Data / Assumptions:

Sanmitra walks 8 m north.
He turns right from facing north and walks 16 m east.
He turns left from facing east and walks 5 m north.
He turns left again from facing north and walks 16 m west.
We need the direction of his final position relative to the starting point.

Concept / Approach:
Use coordinates for clarity. Take the starting point as (0, 0). North increases y, south decreases y, east increases x, and west decreases x. After each movement we update the coordinates and then see in which quadrant the final point lies. If the final x is zero and y is positive, he is directly north of the starting point, and so on.
Step-by-Step Solution:
Start at (0, 0).
Walk 8 m north to reach (0, 8).
Facing north, a right turn leads east; walk 16 m east to reach (16, 8).
Facing east, a left turn leads north; walk 5 m north to reach (16, 13).
Facing north, a left turn leads west; walk 16 m west to reach (0, 13).
Final coordinates are (0, 13), meaning he is directly north of his starting point.
Verification / Alternative check:
Horizontally, Sanmitra moves 16 m east and then 16 m west, which cancel out. Vertically, he moves 8 m north and then another 5 m north, with no southward movement, giving a total of 13 m north. Therefore, his final position is directly north of where he started, without any east west offset.
Why Other Options Are Wrong:
Option A: South would require a net movement downward, which does not occur here. 
Option B: East would require a remaining positive x coordinate, but the net x is zero. 
Option D: West would require a negative x coordinate, which is also not the case. 
Option E: None of these is incorrect because North is explicitly listed and correct.
Common Pitfalls:
One common mistake is assuming that returning 16 m west immediately brings him back to the starting point, ignoring the additional 5 m north that was covered. Another error is misidentifying right and left turns when not initially facing north. A clear x y coordinate tracking eliminates such confusion.
Final Answer:
Sanmitra is finally in the North direction from his starting point.

Question 19

Raj leaves for his office in a car. He drives 15 km towards the north, then 10 km towards the west, then turns towards the south and covers 5 km, and further turns towards the east and moves 8 km. Finally he turns right and drives another 10 km. In …

Accepted Answer

Introduction / Context:
This question describes Raj route with several directional changes and asks for his final direction from his starting point. The sequence of movements partly cancels out, so instead of focusing on the full path length, we should compute the net displacement by separating the horizontal and vertical components of his travel.
Given Data / Assumptions:

Raj drives 15 km north.
He then drives 10 km west.
He then drives 5 km south.
He then drives 8 km east.
Finally, from facing east, he turns right and drives 10 km south.
We must find his final direction from the starting point.

Concept / Approach:
We plot his movement on a coordinate grid. Take the starting point as (0, 0). Driving north increases y, south decreases y, east increases x, and west decreases x. After each segment, we update the coordinates. At the end, we look at the signs of x and y to decide the direction with respect to the starting point. For this question, only the final direction is needed, not the exact distance.
Step-by-Step Solution:
Start at (0, 0).
Go 15 km north to reach (0, 15).
Go 10 km west to reach (-10, 15).
Go 5 km south to reach (-10, 10).
Go 8 km east to reach (-2, 10).
Facing east, a right turn leads south; go 10 km south to reach (-2, 0).
Final coordinates are (-2, 0), which places Raj 2 km to the west of his starting point.
Verification / Alternative check:
Total vertical movement: 15 km north minus 5 km south minus 10 km south equals 0 km, so the net north south displacement is zero. Total horizontal movement: 10 km west minus 8 km east yields 2 km west. Therefore, Raj ends directly to the west of his starting position, confirming the coordinate calculation.
Why Other Options Are Wrong:
Option B: North would require a positive net vertical displacement, which is not present here. 
Option C: South would require a negative net vertical displacement; again, net vertical displacement is zero. 
Option D: East would require a positive net horizontal displacement, but the car ends to the west. 
Option E: None of these is incorrect because West is a listed option and is correct.
Common Pitfalls:
A common mistake is to treat the last right turn from east as leading north instead of south. Another error is failing to account for all vertical movements and assuming Raj remains north of his starting point. Systematically summing horizontal and vertical components avoids such misinterpretations.
Final Answer:
Raj is finally in the West direction from his starting point.

Question 20

Prasad moves 10 km towards the north from his starting point, then turns towards the east and travels 20 km. From there he turns towards the south and continues for another 10 km, and finally he moves 7 km towards the west. How far is he from the st…

Accepted Answer

Introduction / Context:
This is a straightforward distance and displacement problem based on a rectangular path. Prasad moves north, then east, then south, and finally west. The question asks for his straight line distance from the starting point after the entire journey, which is essentially the magnitude of his net displacement vector.
Given Data / Assumptions:

Prasad travels 10 km north.
He then travels 20 km east.
He then travels 10 km south.
He finally travels 7 km west.
All movements are in straight lines and at right angles.

Concept / Approach:
We represent the movements on a coordinate plane. Let the starting point be (0, 0). North adds to y, south subtracts from y, east adds to x, and west subtracts from x. After computing the final coordinates, we use the distance formula distance = sqrt(x^2 + y^2) to find how far Prasad is from the starting point. Observing that some vertical movements cancel makes the calculation easier.
Step-by-Step Solution:
Start at (0, 0).
Move 10 km north to (0, 10).
Move 20 km east to (20, 10).
Move 10 km south to (20, 0).
Move 7 km west to (13, 0).
Final coordinates relative to start: (13, 0).
Straight line distance from start = sqrt(13^2 + 0^2) = 13 km.
Verification / Alternative check:
The 10 km north and 10 km south movements cancel, leaving no net vertical displacement. Horizontally, he moves 20 km east and then 7 km west, giving a net of 13 km east. Since there is no vertical separation, his distance from the starting point is simply 13 km, directly towards the east.
Why Other Options Are Wrong:
Option A: 10 km likely comes from misreading only the first northward leg as the displacement. 
Option C: 3 km is the difference between 10 and 7, not between 20 and 7, and does not reflect the overall path. 
Option D: 17 km is not supported by the net horizontal and vertical movements. 
Option E: None of these is incorrect because 13 Km appears explicitly and is correct.
Common Pitfalls:
Learners sometimes sum all distances to estimate displacement or use the wrong pair of movements when subtracting. Another mistake is forgetting that the north and south segments are equal and cancel. Breaking the path into horizontal and vertical components before computing displacement is a reliable method.
Final Answer:
Prasad is 13 Km away from his starting point.

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