Question 1

P starts walking from the north towards the south. She then turns right at a right angle and walks in that direction, and after that she again turns right at a right angle and walks further. In which direction is she ultimately walking?

Accepted Answer

Introduction / Context:
This direction sense question focuses purely on the final orientation of P after a sequence of right angle turns. Distances are not specified because they are irrelevant to the final direction of movement. The problem tests the ability to mentally track right turns starting from an initial southward direction.
Given Data / Assumptions:

P starts by walking from north towards south, so her initial facing direction is south.
She then turns right at a right angle and walks in that new direction.
She again turns right at a right angle and continues walking.
We only need the final direction she is facing, not how far she has travelled.

Concept / Approach:
When a person is facing a cardinal direction, a right turn means rotating 90 degrees clockwise. Starting from south, a right turn leads to west, and another right turn from west leads to north. Tracking only the facing direction at each stage, without worrying about distances, is enough to answer the question correctly.
Step-by-Step Solution:
Initial facing direction: south.
First right turn: from south, turning right (clockwise) leads to west.
Second right turn: from west, turning right again leads to north.
Therefore, after the two right turns, P is facing north.
Verification / Alternative check:
Visualize the four directions in clockwise order: north, east, south, west. Starting at south, a right turn moves to west, and another right turn moves to north. This confirms that two successive right turns from south lead to north. No distances are needed to determine this orientation.
Why Other Options Are Wrong:
Option B: East would be obtained from north by a right turn, not from south by two right turns. 
Option C: South is the initial direction, not the final one. 
Option D: West is only the intermediate direction after the first right turn. 
Option E: None of these is incorrect because North is clearly listed and matches the reasoning.
Common Pitfalls:
A frequent mistake is to imagine turns relative to the page rather than relative to the person orientation, leading to incorrect mapping of right and left. Another error is to consider only one turn instead of both. Drawing a small compass and marking each turn step by step is an effective way to avoid such confusion.
Final Answer:
P is ultimately walking towards the North.

Question 2

Prabhu travels from his house to the house of his friend, covering a distance of 20 km in a straight line. After some time he leaves his friend house, turns to his right and travels 15 km to reach a park. After resting for a while, he again starts, …

Accepted Answer

Introduction / Context:
This question is a classic example of a direction sense and displacement problem. Instead of only tracking how much total distance Prabhu walks, we are interested in where he finally lands with respect to his home. The task is to visualise his path step by step and then calculate how far his current position is from the starting point, that is, his home. Understanding such questions helps strengthen spatial reasoning, basic coordinate ideas, and the difference between path length and shortest straight line distance, which is also called displacement.

Given Data / Assumptions:

Prabhu travels 20 km in a straight line from his house to the house of his friend.
From his friend house he turns right and travels 15 km to reach a park.
From the park he again turns right and travels 18 km to reach a petrol bunk.
From the petrol bunk he again turns right and covers 15 km.
All turns are right angle turns and all roads are assumed to be straight and on a flat plane.
We assume he initially starts in the east direction for convenience, which does not affect the final distance calculation.

Concept / Approach:
To solve this, we imagine or sketch Prabhu path on a coordinate grid. We assume he first moves east, then apply each right turn to decide the new direction. By converting each move into horizontal and vertical components, we can track his final coordinates relative to the starting point. Once the final coordinate is known, the straight line distance from the origin can be found. In this particular case, because he ends up directly east or west of the starting point, the displacement can be read directly from the horizontal component, without using the Pythagoras theorem.

Step-by-Step Solution:
Step 1: Assume Prabhu starts from his home at the origin point, say (0, 0), and initially walks 20 km towards the east, reaching the friend house at (20, 0).
Step 2: From the friend house he turns right. A right turn from east means he now faces south and walks 15 km, reaching the park at (20, -15).
Step 3: From the park he again turns right. Facing south, a right turn makes him face west. He travels 18 km west and reaches the petrol bunk at (20 - 18, -15) which is (2, -15).
Step 4: From the petrol bunk he once more turns right. Facing west, a right turn makes him face north, and he travels 15 km north to reach (2, -15 + 15) which is (2, 0).
Step 5: His final position is (2, 0), while his home is still at (0, 0). Therefore, he is 2 km east of his home.
Step 6: To reach home, he only needs to travel 2 km directly west in a straight line.

Verification / Alternative check:
An alternative way without coordinates is to notice that the three consecutive right turns form almost a rectangular loop for the 15 km sides. The north and south movements of 15 km cancel out each other. Along the east west line, he first went 20 km east, then effectively 18 km back towards the west, so the net result is that he is 2 km to the east of his home. Therefore, he must cover 2 km more to reach his home. This cross check confirms the coordinate method result.

Why Other Options Are Wrong:
The option 18 km is incorrect because it ignores the cancellation of some segments and mixes total distance walked with displacement. The option 21 km is wrong because it might come from subtracting or adding the wrong pair of distances. The option 23 km is incorrect as it assumes a mistaken net distance or uses total path length ideas instead of shortest distance. None of these values correspond to the actual horizontal separation of 2 km between his final point and his home.

Common Pitfalls:
A frequent mistake in such questions is to add all distances and assume that the result is the answer, which confuses total distance travelled with shortest straight line distance from the starting point. Another common error is mixing up the directions when turning right or left, especially after more than one turn. Forgetting that north cancels south and east cancels west when the magnitudes match is another key source of error. Drawing a neat diagram or using a simple coordinate approach helps avoid these pitfalls.
Final Answer:
The required straight line distance from his current position back to his home is 2 km.

Question 3

Vijey first walks 10 metres towards the west from his starting point, then turns left and walks another 10 metres, again turns left and walks 10 metres along the new direction, and finally makes a 45 degree turn to his right and continues walking st…

Accepted Answer

Introduction / Context:
This problem tests direction sense with both right and left turns and finally a turn by 45 degrees. Rather than asking for where Vijey ends up, the question asks for the direction in which he is walking after the last turn. Such questions are common in verbal reasoning exams and they check whether you can precisely track orientation changes step by step without getting confused by multiple turns.
Given Data / Assumptions:

Vijey initially walks 10 metres towards the west from his starting point.
From there, he turns left and walks 10 metres.
He again turns left and walks another 10 metres.
Finally, he turns 45 degrees towards his right and walks straight.
All directions are with respect to the standard compass directions: North, South, East, and West.
The ground is assumed flat and straight lines are followed in each segment.

Concept / Approach:
The key idea is to track orientation, not only position. When a person is facing a certain cardinal direction, left and right turns give predictable new directions: from West, left means South and right means North; from South, left means East and right means West; from East, left means North and right means South; from North, left means West and right means East. A turn of 45 degrees from a main direction leads to one of the intercardinal directions like North East, South East, South West, or North West.
Step-by-Step Solution:
Step 1: Initially, Vijey walks west, so at that moment he is facing West.
Step 2: From facing West, he turns left. A left turn from West means he now faces South. He then walks 10 metres in the South direction.
Step 3: From facing South, he again turns left. A left turn from South leads him to face East. He now walks 10 metres towards the East.
Step 4: At this point, just before the last turn, he is facing East.
Step 5: From facing East, he takes a 45 degree turn towards his right. A right turn from East goes towards South. A full right angle from East is South; half of that, that is 45 degrees, corresponds to the diagonal direction exactly between East and South, which is South East.
Step 6: Therefore, after the final 45 degree right turn, he is walking in the South East direction.

Verification / Alternative check:
You can verify this by drawing compass directions on paper. Mark East, then draw a right angle towards South and split that quarter circle into two equal parts. The direction halfway between East and South is South East. Since he was facing East and turned 45 degrees to the right, he must now be walking along that South East diagonal, confirming the reasoning above.
Why Other Options Are Wrong:
South is wrong because that would require a full 90 degree right turn from East, not 45 degrees. West is incorrect because the last orientation before the 45 degree turn is East, and a small right turn from East can never give West. South West is also wrong, because South West is between South and West, whereas his final direction is between East and South, which defines South East.
Common Pitfalls:
Common mistakes include misinterpreting left and right after several turns, forgetting the current facing direction, or confusing 45 degree turns with full 90 degree turns. Some students also forget that South East lies between South and East, not between South and West. Maintaining a clear mental or sketched diagram of each orientation step helps avoid these errors.
Final Answer:
After all the given movements and turns, Vijey is finally walking towards the South East direction.

Question 4

A woman first walks 3 km towards the north from her starting position, then turns towards the west and walks 4 km, after that she turns towards the south and walks 7 km, and finally she turns to her left and walks another 4 km. Based on this sequenc…

Accepted Answer

Introduction / Context:
This question evaluates understanding of basic direction sense and net displacement. The woman makes several moves in different directions, and we are asked to find her final position relative to the starting point, not the total distance that she has walked. Solving this requires careful tracking of movements along the north south and east west axes, and recognising that some movements cancel out partially or fully.
Given Data / Assumptions:

The woman walks 3 km towards the north from her starting point.
She then turns west and walks 4 km.
Next, she turns south and walks 7 km.
Finally, she turns to her left and walks 4 km.
Left and right are with respect to the direction in which she is currently facing at that moment.
All paths are straight and on level ground, and distances are accurate.

Concept / Approach:
We break her path into horizontal (east west) and vertical (north south) components. Movements towards the north are considered positive on the vertical axis, movements towards the south negative. Movements towards the east are positive on the horizontal axis, and movements towards the west are negative. After each segment we update the position. At the end we compare the final coordinates with the starting point to determine the net displacement in both magnitude and direction.
Step-by-Step Solution:
Step 1: Start at the origin (0, 0). After walking 3 km north, her position becomes (0, 3).
Step 2: From there she turns west and walks 4 km. Moving west decreases the horizontal coordinate, so the new position is (−4, 3).
Step 3: She then turns south and walks 7 km. Moving south reduces the vertical coordinate by 7, so the new position is (−4, 3 − 7) = (−4, −4).
Step 4: At this moment she is facing south. Turning left from south means she will face east. She now walks 4 km east. Moving 4 km east increases the horizontal coordinate by 4, so the new position is (−4 + 4, −4) = (0, −4).
Step 5: Her final coordinates are therefore (0, −4). The starting point was (0, 0). So she is 4 km south of her starting position.

Verification / Alternative check:
Notice that she moved 3 km north and later 7 km south. The net vertical movement is 7 − 3 = 4 km south. For horizontal movement, she walked 4 km west and later 4 km east, which cancel each other, leaving zero net horizontal displacement. So the only remaining net effect is 4 km towards the south, which confirms that she is exactly 4 km south of her starting point.
Why Other Options Are Wrong:
The option 10 km south is wrong because it adds some distances instead of considering cancellation. The options 4 km north and 10 km north reverse the direction and ignore that she walked a greater distance south than north. They do not represent the correct net movement. Hence only 4 km south matches the calculated displacement.
Common Pitfalls:
A common mistake is to confuse total distance travelled with displacement. Another typical error is to misinterpret the final left turn, especially when turning from south. Some test takers also forget to cancel equal east and west movements. Drawing a simple diagram with arrows or using a small coordinate system on paper significantly helps in avoiding these pitfalls.
Final Answer:
The woman is now located 4 km south of her original starting position.

Question 5

A migrating bird first flies 40 km towards the north from its initial position, then turns towards the east and flies 50 km, then turns again towards the north and flies another 110 km, and finally turns to its left and flies 50 km. Based on this co…

Accepted Answer

Introduction / Context:
This problem deals with a sequence of movements in different directions and asks for the final position relative to the starting point. It uses distances in kilometres and simple cardinal directions, which makes it a straightforward displacement question once the movements are broken into their horizontal and vertical components. These types of questions commonly appear under direction sense and basic analytical reasoning sections.
Given Data / Assumptions:

The bird flies 40 km north from the starting point.
It then turns east and flies 50 km.
Next, it turns north and flies 110 km more.
Finally, it turns to its left and flies 50 km.
Turning left is defined relative to the current direction of motion.
All flights are in straight lines and on a flat reference plane.

Concept / Approach:
We treat the starting point as the origin of a coordinate system. Movements towards the north and south affect the vertical coordinate, while movements towards the east and west affect the horizontal coordinate. Turning left from a given direction moves to the adjacent direction in the anticlockwise sense. After computing the final coordinates, we compare them with the starting point to obtain the net displacement and direction.
Step-by-Step Solution:
Step 1: Assume the starting point is (0, 0). After flying 40 km north, the bird reaches (0, 40).
Step 2: It then turns east and flies 50 km, so the new position becomes (50, 40).
Step 3: Now facing east, it turns north and flies another 110 km. Moving 110 km north increases the vertical coordinate to 40 + 110 = 150, giving the position (50, 150).
Step 4: At this moment the bird is flying north. A left turn from north makes it face west. It then flies 50 km west, which reduces the horizontal coordinate from 50 to 0, placing it at (0, 150).
Step 5: The starting point is (0, 0), and the final point is (0, 150). Therefore, the bird is 150 km directly north of its starting position.

Verification / Alternative check:
We can verify by looking at the net north south displacement. The bird has flown 40 km north and then 110 km north: a total of 150 km north. There is no southward motion at any stage, so the net vertical displacement is 150 km north. For the horizontal displacement, it flies 50 km east and subsequently 50 km west, which cancel each other out. Thus, only 150 km north remains as net displacement, confirming the result.
Why Other Options Are Wrong:
The options 150 km south and 70 km south reverse the correct direction, which contradicts the fact that there is no southward movement at all. The option 70 km north is inconsistent with the sum of the two legs towards the north, which clearly add up to 150 km. Therefore none of these alternatives match the correctly calculated displacement.
Common Pitfalls:
Many learners incorrectly add east and west distances without cancelling them, or mix up the left turn directions. Another error is to misread the distances and add only part of the northbound legs. Precisely listing each move and keeping track of net east west and net north south distances separately is crucial for accuracy.
Final Answer:
The migrating bird is now located 150 km north of its starting point.

Question 6

A paper boy on his cycle first travels 10 km towards the east from his starting point, then turns towards the south and cycles 3 km, then turns towards the west and cycles 6 km, and finally turns to his right and cycles another 3 km. Taking all thes…

Accepted Answer

Introduction / Context:
This question is about direction sense and net position after a series of movements. The paper boy changes direction multiple times and we need to determine where he finishes relative to where he started. It tests the ability to decompose movements into horizontal and vertical components and to understand how right turns affect direction.
Given Data / Assumptions:

The paper boy cycles 10 km towards the east.
He then turns south and cycles 3 km.
Next, he turns west and cycles 6 km.
Finally, he turns to his right and cycles 3 km.
Right is defined with respect to his current facing direction.
All paths are straight and taken on level ground with no elevation changes.

Concept / Approach:
We use a coordinate system based approach. Movements to the east and west only affect the horizontal coordinate, and movements to the north and south only affect the vertical coordinate. The idea is to compute the net east west and net north south displacements separately, and then determine the final position. The last right turn requires careful attention to the direction he is facing at that moment.
Step-by-Step Solution:
Step 1: Assume his starting position is (0, 0). Moving 10 km east shifts him to (10, 0).
Step 2: From there he turns south and cycles 3 km, reducing the vertical coordinate. His new position becomes (10, −3).
Step 3: Now he turns west and cycles 6 km, reducing the horizontal coordinate by 6. He reaches (10 − 6, −3) which is (4, −3).
Step 4: At this point he is facing west. A right turn from west makes him face north. He then cycles 3 km north. Moving north increases the vertical coordinate from −3 to 0, so the final position is (4, 0).
Step 5: The starting point is (0, 0), so he ends up 4 km to the east of his starting point and at the same north south level.

Verification / Alternative check:
Look at the net east west displacement: he first goes 10 km east and later 6 km west. The net is 10 − 6 = 4 km east. For north south displacement, he travels 3 km south and then 3 km north, which exactly cancel out, leaving zero net vertical displacement. So his final position must be 4 km east of the start with no north or south offset, which confirms the coordinate calculation.
Why Other Options Are Wrong:
The option 4 km west is opposite to the correctly calculated net eastward displacement. The options 14 km east and 14 km west come from adding distances without cancelling opposite directions and therefore represent total or incorrect path length rather than net displacement. None of them match the actual final position.
Common Pitfalls:
Learners often sum all east and west distances or forget to cancel equal north south movements. Another mistake is misinterpreting the last right turn from west as south instead of north. Keeping a small directional diagram and marking each leg carefully usually prevents these errors.
Final Answer:
The paper boy is finally located 4 km east of his starting position.

Question 7

A plane first flies 100 km towards the west from its starting point, then turns towards the south and flies 150 km, then turns again towards the west and flies another 300 km, and finally turns to its right and flies 150 km. After completing all the…

Accepted Answer

Introduction / Context:
This is another displacement and direction sense question, but with larger distances that resemble the route of an aircraft. The goal is to find the final position of the plane relative to the starting point after flying several legs in different directions. Only by analysing the net horizontal and vertical movements can we identify both the correct distance and the correct direction.
Given Data / Assumptions:

The plane flies 100 km towards the west from its starting point.
It then turns south and flies 150 km.
Next, it turns west again and flies 300 km.
Finally, it turns to its right and flies 150 km.
Right is defined relative to its current flight direction at that moment.
The flight is assumed to be in a horizontal plane relative to the map directions without changes in altitude affecting the calculation.

Concept / Approach:
We model the starting point as the origin in a coordinate system. Movements west decrease the horizontal coordinate, east increases it, south decreases the vertical coordinate, and north increases it. Right turns are always made relative to the aircraft current heading. When it has moved equal distances south and north, those effects cancel out, leaving a purely east west displacement. Our task is to compute that net displacement.
Step-by-Step Solution:
Step 1: Start at (0, 0). Flying 100 km west brings the plane to (−100, 0).
Step 2: The plane then turns south and flies 150 km, reaching (−100, −150).
Step 3: Next, it turns west again and flies 300 km, so the horizontal coordinate decreases by another 300. The new position is (−100 − 300, −150) = (−400, −150).
Step 4: At this point, the plane is facing west. A right turn from west means it now faces north. It then flies 150 km north, which increases the vertical coordinate from −150 to 0, so the final position becomes (−400, 0).
Step 5: The starting point was (0, 0). Therefore, the plane is now 400 km west of the starting point with no net north south displacement.

Verification / Alternative check:
Consider the north south movements. The plane goes 150 km south and later 150 km north, which completely cancel out. In the east west direction, it travels 100 km west and then an additional 300 km west, with no eastward movement at all. Thus the total westward displacement is 100 + 300 = 400 km. This directly confirms that the final position is 400 km west of the origin.
Why Other Options Are Wrong:
The options 400 km east and 200 km east reverse the actual direction, which is west. The options 200 km west and 200 km east reflect partial calculations where only part of the westward journey is considered or the cancellation of north and south movements is mishandled. Therefore, none of these represent the full net displacement correctly except 400 km west.
Common Pitfalls:
Common errors include ignoring that equal north and south movements negate each other, and mistakenly subtracting only part of the westward legs. Some test takers also confuse the right turn from west, assuming it leads to south instead of north. Drawing a simple diagram of the path helps maintain clarity.
Final Answer:
The plane is now located 400 km west of its starting position.

Question 8

A and B start running from the same point. A runs 3 km towards the west, then turns towards the south and runs 5 km, and then turns to her right and runs 7 km. B runs 1 km towards the south, then turns to her right and runs 10 km. After all these mo…

Accepted Answer

Introduction / Context:
This direction sense problem involves two people, A and B, who run different paths starting from the same point. We are not asked for their positions relative to the starting point, but specifically for the position of B with respect to A. This requires computing both final coordinates and then subtracting to get the relative displacement vector from A to B.
Given Data / Assumptions:

A runs 3 km towards the west from the starting point.
A then turns south and runs 5 km.
A then turns to her right and runs 7 km.
B runs 1 km towards the south from the starting point.
B then turns to her right and runs 10 km.
Right turns are defined relative to the current facing direction of the runner.
All movements are on straight, level ground.

Concept / Approach:
We assign a coordinate system with the starting point at (0, 0). Using this, we calculate the final coordinates of A and B separately. A westward movement decreases the horizontal coordinate, while eastward movement increases it. Similarly, north and south movements affect the vertical coordinate positively or negatively. Once we have the coordinates of A and B, we find the displacement from A to B by subtracting A position from B position and interpret the resulting vector as direction and distance.
Step-by-Step Solution:
Step 1: Track A. From (0, 0) A runs 3 km west to (−3, 0).
Step 2: A turns south and runs 5 km, reaching (−3, −5).
Step 3: A then turns right. Facing south, a right turn makes her face west. She runs 7 km west, reaching (−3 − 7, −5) = (−10, −5).
Step 4: Now track B. From (0, 0) B runs 1 km south to (0, −1).
Step 5: B then turns right. Facing south, a right turn means B faces west. B runs 10 km west to reach (−10, −1).
Step 6: A final position is (−10, −5). B final position is (−10, −1). From A to B, the horizontal coordinate is the same and the vertical changes from −5 to −1, which is a movement of 4 km towards the north.

Verification / Alternative check:
Notice that both A and B end up on the same vertical line: each is 10 km west of the starting point. The only difference is their north south coordinate. A is 5 km south of the origin and B is 1 km south of the origin. Thus B is 4 km north of A. This matches the coordinate calculation and provides a simple visual interpretation if you sketch the points on paper.
Why Other Options Are Wrong:
The options mentioning 4 km south or 6 km south reverse the actual relative direction. The distances of 6 km north or south arise from miscalculating one of the vertical displacements, such as mistaking A southward run length or mixing up B path. Only 4 km north correctly reflects the difference between the two final vertical positions.
Common Pitfalls:
A frequent error is to compute each runner position relative to the origin but then forget to take their difference. Some learners also misapply right turns or confuse the path segments. Always carefully write down A and B coordinates and then compute B minus A to get the relative position.
Final Answer:
B is located 4 km north of A.

Question 9

A woman in a shopping complex walks 150 m towards the east from her starting position, then turns towards the north and walks 180 m, then turns towards the west and walks 70 m, and finally turns to her left and walks another 180 m. After completing …

Accepted Answer

Introduction / Context:
This question involves a sequence of rectangular movements and a final left turn in a shopping complex. The goal is to determine the net displacement of the woman from her starting point, not the total path length she has walked. It requires keeping track of the horizontal and vertical components and understanding the effect of turns on direction.
Given Data / Assumptions:

The woman walks 150 m east from her starting position.
She then turns north and walks 180 m.
Next, she turns west and walks 70 m.
Finally, she turns to her left and walks 180 m.
Left is defined relative to the direction in which she is currently facing.
All paths are straight and on flat ground.

Concept / Approach:
We employ a coordinate system where east west affects the horizontal axis and north south affects the vertical axis. Turning to the left rotates the direction 90 degrees anticlockwise. After calculating the final coordinates, we compare them to the starting coordinates to find the net displacement, which gives both magnitude and direction of her final position relative to the origin.
Step-by-Step Solution:
Step 1: Start at (0, 0). Walking 150 m east takes her to (150, 0).
Step 2: She then turns north and walks 180 m, reaching (150, 180).
Step 3: Next, she turns west and walks 70 m, reducing the horizontal coordinate to 150 − 70 = 80, giving the position (80, 180).
Step 4: At this moment she is facing west. A left turn from west makes her face south. She then walks 180 m south, reducing the vertical coordinate from 180 to 0. The final position becomes (80, 0).
Step 5: Comparing (80, 0) with the starting point (0, 0) shows that she is 80 m east of her original position with no north south displacement.

Verification / Alternative check:
Consider the north south movements: she walks 180 m north and then 180 m south, so these cancel, leaving zero net north south movement. For east west movements, she walks 150 m east and 70 m west, resulting in a net eastward displacement of 80 m. This simple balancing check confirms the coordinate calculation and reinforces the understanding that cancelling movements is key in such problems.
Why Other Options Are Wrong:
The options 80 m west and 220 m west incorrectly reverse the direction or combine distances in an incorrect way. The option 220 m east looks like a sum of some segments rather than a net result. None of these match the calculated net displacement of 80 m east from the origin.
Common Pitfalls:
Typical errors include misinterpreting the final left turn from west, leading to a wrong final direction, and forgetting that equal north and south movements cancel each other. Some also add distances without considering opposing directions. Careful diagramming and stepwise calculation prevent these mistakes.
Final Answer:
She is now located 80 m east of her starting position.

Question 10

A boy is initially travelling towards the west. He first turns to his right, continues in that new direction, and then again turns to his left. After performing these two turns in sequence, in which cardinal direction is the boy finally facing?

Accepted Answer

Introduction / Context:
This is a pure direction sense question that focuses only on changes in orientation, not on distances or coordinates. The boy begins by facing west, then performs a right turn followed by a left turn. The problem tests understanding of relative right and left turns from different starting directions and the effect of successive turns.
Given Data / Assumptions:

The boy initially travels towards the west, so he is facing west.
He then turns to his right once.
After moving in that new direction, he turns to his left once.
No specific distances are given or needed because only direction is asked.
All turns are right angle turns of 90 degrees.

Concept / Approach:
We use cardinal directions and right angle turns. When facing West, a right turn leads to North, and a left turn from West leads to South. When facing North, a left turn leads to West and a right turn leads to East. Since the second turn is taken after the first one, we must track the orientation after each step and not confuse it with the initial facing direction.
Step-by-Step Solution:
Step 1: The boy starts facing West.
Step 2: He makes a right turn. A right turn from West leads to the North direction, so he now faces North.
Step 3: From this new orientation of facing North, he then makes a left turn. A left turn from North leads to West.
Step 4: Therefore, after both turns, the boy ends up facing West again.

Verification / Alternative check:
You can visualise this by drawing a cross of four directions: North at the top, South at the bottom, East to the right, and West to the left. Mark the rotation step by step. From West, move to North (right turn), then from North move back to West (left turn). This clearly shows that the final direction matches the initial direction.
Why Other Options Are Wrong:
South and East are incorrect because the described sequence of one right turn and one left turn does not lead to them from an initial West direction. North is the intermediate direction after the first right turn, but the second left turn takes the boy away from North and back to West. Hence, only West is consistent with the correct turning sequence.
Common Pitfalls:
A common pitfall is to cancel a right and a left turn mentally and assume the boy continues to face his original direction without checking the order of turns and directions. Another mistake is to apply both turns relative to the starting direction instead of updating the facing direction after the first turn. Practising with simple diagrams helps avoid these errors.
Final Answer:
After turning right once and then turning left once, the boy is facing West.

Question 11

A pilot takes off from a point and flies 35 km towards the west, then turns towards the south and flies 15 km, then turns to the left and flies 20 km, and finally turns towards the north and flies 15 km. After completing these legs of the journey, w…

Accepted Answer

Introduction / Context:
This direction sense problem simulates the flight path of a plane making rectangular turns. The goal is to determine the net displacement of the plane from its starting location, not the total distance flown. It tests whether you can correctly interpret left turns from different directions and then combine east west and north south movements correctly.
Given Data / Assumptions:

The plane first flies 35 km towards the west.
It then turns south and flies 15 km.
Next, it turns to its left and flies 20 km.
Finally, it turns towards the north and flies 15 km.
The left turn in the third step is taken from the current direction at that instant.
All flights occur in a horizontal plane and follow straight line segments.

Concept / Approach:
We apply a coordinate based approach. West and east movements modify the horizontal coordinate, while north and south movements modify the vertical coordinate. Turning left from south leads to east, while turning left from east would lead to north, and so on. We compute each leg in sequence to obtain the final coordinates, then compare with the origin to get the net displacement and direction.
Step-by-Step Solution:
Step 1: Place the starting point at (0, 0). After flying 35 km west, the plane is at (−35, 0).
Step 2: It then turns south and flies 15 km, reaching (−35, −15).
Step 3: At this point the plane is facing south. A left turn from south makes it face east. It then flies 20 km east, which increases the horizontal coordinate from −35 to −15, giving position (−15, −15).
Step 4: Finally, it turns towards the north and flies 15 km. Moving 15 km north raises the vertical coordinate from −15 to 0, so the final position is (−15, 0).
Step 5: The starting point is (0, 0). Therefore, the plane is now 15 km to the west of the starting point.

Verification / Alternative check:
Look at the north south movements: 15 km south followed by 15 km north cancel out exactly, leaving no net vertical displacement. For the east west movements, the plane goes 35 km west and then 20 km east. The net displacement is 35 − 20 = 15 km west. There are no other horizontal components. This confirmatory check supports the coordinate calculation.
Why Other Options Are Wrong:
The options 55 km west and 55 km east arise if someone mistakenly adds 35 km and 20 km or mixes direction signs. The option 15 km east reverses the correct net direction, and ignores that the westward leg is longer than the eastward leg. Only 15 km west matches the accurate net movement from the start.
Common Pitfalls:
Errors commonly arise from misinterpreting the left turn from south as going west instead of east, or from forgetting to cancel equal north and south legs. Others mistakenly add distances in opposite directions instead of subtracting. Careful orientation tracking or sketching a diagram makes such puzzles much easier.
Final Answer:
The plane ends up 15 km west of its starting position.

Question 12

A man is initially facing towards the east. He turns towards the north and walks 5 km, and then turns 270 degrees in the anticlockwise direction and walks another 12 km. What is the minimum straight line distance between his initial starting positio…

Accepted Answer

Introduction / Context:
This question combines angle based turning with distance movement, and it asks for the minimum distance between the initial and final positions. This minimum distance is the straight line distance between the two locations, which can be found using basic geometry once we know the coordinates of the final point. Understanding how a 270 degree anticlockwise turn affects direction is crucial here.
Given Data / Assumptions:

The man is initially facing east.
He turns towards the north and walks 5 km.
After that he turns 270 degrees anticlockwise.
He then walks another 12 km in the new direction after the 270 degree anticlockwise turn.
The ground is taken as flat and all moves are straight line segments.

Concept / Approach:
First we determine his direction after each turn. A turn of 90 degrees anticlockwise changes direction by one step in the north west south east cycle. A turn of 270 degrees anticlockwise is equivalent to turning 90 degrees clockwise. Once we know his final direction, we can break the path into vertical and horizontal components. The straight line distance between the starting and ending points can then be computed using the Pythagoras theorem as the hypotenuse of a right triangle.
Step-by-Step Solution:
Step 1: The man starts facing east. He first turns towards north. This is a 90 degree anticlockwise turn from east and he walks 5 km in the north direction, reaching (0, 5) if we set the origin at the starting point.
Step 2: From facing north, he then turns 270 degrees anticlockwise. A 270 degree anticlockwise rotation is the same as a 90 degree clockwise rotation. From north, a 90 degree clockwise turn makes him face east.
Step 3: He now walks 12 km towards the east. Starting from (0, 5), moving 12 km east places him at (12, 5).
Step 4: The starting position is (0, 0). The final position is (12, 5). The straight line distance between these two points is the hypotenuse of a right triangle with legs 12 and 5.
Step 5: Using Pythagoras theorem, distance^2 = 12^2 + 5^2 = 144 + 25 = 169.
Step 6: Therefore, distance = square root of 169 = 13 km.

Verification / Alternative check:
Visually, you can sketch a point, move 5 units up for the northward walk, and then 12 units to the right for the eastward walk. This forms a right triangle with a base of 12 and height of 5. Even without full calculation, you may recall the 5 12 13 Pythagorean triple, which confirms that the hypotenuse is 13 units. This matches the computed value and ensures the calculation is consistent.
Why Other Options Are Wrong:
The options 17 km, 11 km, and 9 km do not satisfy the Pythagoras relationship for the legs of 5 km and 12 km. For example, 11^2 = 121 and 9^2 = 81, both of which do not equal 169 when squared. Only 13 km correctly fits the 5 12 13 relationship and corresponds to the exact distance between (0, 0) and (12, 5).
Common Pitfalls:
Some test takers mistakenly treat a 270 degree anticlockwise turn as if it were 90 degrees anticlockwise, leading to a different direction and wrong coordinates. Others forget to apply the Pythagoras theorem or incorrectly add distances. Recognising that 270 degrees anticlockwise equals 90 degrees clockwise is a key conceptual step here.
Final Answer:
The minimum straight line distance between his starting and ending positions is 13 km.

Question 13

Ram travels 5 km towards the east from his original position, then takes a left turn and travels 10 km, then takes a right turn and travels another 5 km, and finally takes another right turn and covers 10 km. After this complete route, how far is he…

Accepted Answer

Introduction / Context:
The problem describes Ram walking in a sequence that forms a kind of rectangular path, with multiple left and right turns. The task is to find how far he is from his starting point after completing the entire journey. This is a displacement question, not a total distance question, and it requires tracking his position step by step in terms of coordinates.
Given Data / Assumptions:

Ram starts from a point and travels 5 km towards the east.
He then takes a left turn and travels 10 km.
Next, he takes a right turn and travels another 5 km.
Finally, he takes another right turn and travels 10 km.
Left and right turns are of 90 degrees and are relative to the current direction of motion.
The terrain is flat and straight line paths are followed.

Concept / Approach:
We choose a coordinate system where east west movement affects the horizontal axis and north south movement affects the vertical axis. Each leg of the journey updates Ram coordinates. At the end we compute the displacement between the final and initial coordinates. In this particular case, the path effectively forms a rectangular loop that does not fully close, so only one coordinate ends up non zero.
Step-by-Step Solution:
Step 1: Set the starting point as (0, 0). After Ram travels 5 km east, his position is (5, 0).
Step 2: From facing east, a left turn makes him face north. He now travels 10 km north, reaching (5, 10).
Step 3: From facing north, a right turn makes him face east. He travels 5 km east to (10, 10).
Step 4: From facing east, another right turn makes him face south. He travels 10 km south to (10, 0).
Step 5: The final position is (10, 0) and the starting position is (0, 0). Therefore, he is 10 km east of his starting point.

Verification / Alternative check:
You can also observe that his total northward movement of 10 km is exactly balanced by his total southward movement of 10 km, so there is no net north south displacement. In the east west direction, he goes 5 km east and later another 5 km east, with no westward movement. So the net horizontal displacement is 10 km east. This gives the same result as the coordinate method.
Why Other Options Are Wrong:
The options 20 km, 15 km, and 25 km are incorrect because they come from adding lengths of different legs without respecting direction and cancellation. The motion does not place Ram 20 km or 25 km away from the origin, since there is only a net eastward displacement of 10 km and no vertical offset. Therefore, these alternatives do not match the true displacement.
Common Pitfalls:
A common mistake is to think that walking 5 + 10 + 5 + 10 km means he must be 30 km away, which confuses path length with displacement. Another error is misinterpreting left and right turns, especially after more than one change in direction. Using a quick sketch with arrows for each leg helps clarify the correct final position.
Final Answer:
Ram is 10 km away from his original position, directly towards the east.

Question 14

A girl is initially standing facing towards the south. She first turns 135 degrees in the anticlockwise direction, and then again takes a 180 degree turn in the anticlockwise direction. After performing these two rotations, in which direction is she…

Accepted Answer

Introduction / Context:
This question is purely about orientation and rotation in terms of degrees. It asks for the final facing direction of a girl after she turns first 135 degrees anticlockwise from facing south and then another 180 degrees anticlockwise. Correctly handling angles larger than 90 degrees and remembering the relative positions of the eight principal directions is essential.
Given Data / Assumptions:

The girl initially faces south.
She turns 135 degrees anticlockwise.
From that new direction, she again turns 180 degrees anticlockwise.
We use the standard compass with North, East, South, and West, and the four diagonal directions North-east, South-east, South-west, and North-west.
All rotations are in the horizontal plane.

Concept / Approach:
We can represent directions on a circle: East at 0 degrees, North at 90 degrees, West at 180 degrees, and South at 270 degrees. Anticlockwise movement corresponds to increasing angle, while clockwise movement corresponds to decreasing angle. Each 45 degree increment gives an intercardinal direction. By converting rotations into final angles, we can relate them back to the nearest named direction.
Step-by-Step Solution:
Step 1: Represent the initial direction. Facing south corresponds to 270 degrees on the directional circle if East is taken as 0 degrees.
Step 2: First rotation: she turns 135 degrees anticlockwise. Adding 135 degrees to 270 degrees gives 270 + 135 = 405 degrees.
Step 3: Since angles wrap around every 360 degrees, 405 degrees is equivalent to 405 − 360 = 45 degrees. The direction at 45 degrees is North-east.
Step 4: Second rotation: now from North-east (45 degrees), she turns a further 180 degrees anticlockwise. Adding 180 degrees gives 45 + 180 = 225 degrees.
Step 5: The direction of 225 degrees lies exactly halfway between South (270 degrees) and West (180 degrees), so it is the South-west direction.

Verification / Alternative check:
You can check using quadrant thinking. From South, a 90 degree anticlockwise turn leads to West, and an additional 45 degrees leads to North-west. However, we need 135 degrees, which carries her to North-east due to wrapping around the circle past West and North. Rotating another 180 degrees from North-east places her diagonally opposite, that is, pointing to South-west, which is consistent with the angle based method.
Why Other Options Are Wrong:
South would be correct only if the final net rotation were a multiple of 360 degrees from the initial direction, which it is not. South-east and West correspond to angles of 135 degrees and 180 degrees from East respectively, which do not match the calculated 225 degrees final angle. Thus, they do not represent the correct final orientation.
Common Pitfalls:
Mistakes often come from treating 135 degrees as 90 degrees, from miscounting anticlockwise versus clockwise, or from forgetting to wrap angles greater than 360 degrees. Another pitfall is confusing North-east with North-west when working with diagonal directions. Drawing a circle with marked angles greatly helps to avoid such confusion.
Final Answer:
After both anticlockwise turns, the girl is facing the South-west direction.

Question 15

A boy leaves his school and first travels 8 km towards the east. He then takes a left turn and travels 6 km in that direction, after which he turns towards the east again and travels another 5 km. Finally, he takes a right turn and travels 10 km. In…

Accepted Answer

Introduction / Context:
This direction sense problem describes a multi step path taken by a boy leaving his school. We are asked for the direction of his final position as seen from the school. As with many such questions, the key is to track all east west and north south components and then determine which quadrant of the compass the final point lies in relative to the start.
Given Data / Assumptions:

The boy walks 8 km east from his school.
He then takes a left turn and walks 6 km in that direction.
After that he turns towards the east and walks another 5 km.
Finally, he takes a right turn and walks 10 km.
Left and right are relative to his current direction, and all turns are right angled turns.
The ground is flat and all distances are accurate.

Concept / Approach:
We track his path using coordinates. East west movements change the horizontal coordinate, and north south movements change the vertical coordinate. After determining the final coordinates of his position relative to the school, we look at the signs of the horizontal and vertical values to decide whether he is in the North-east, South-east, South-west, or North-west quadrant relative to the school.
Step-by-Step Solution:
Step 1: Set the school at (0, 0). After the boy walks 8 km east, he is at (8, 0).
Step 2: From facing east, a left turn makes him face north. He walks 6 km north, so his position becomes (8, 6).
Step 3: Next he turns towards the east again, which sets his direction to east, and he walks 5 km. His new position is (8 + 5, 6) = (13, 6).
Step 4: Now he is facing east. A right turn from east makes him face south. He then walks 10 km south, reducing the vertical coordinate to 6 − 10 = −4, so his final position is (13, −4).
Step 5: The x coordinate is positive and the y coordinate is negative, which means he is to the east and south of the school, that is, in the South-east direction from his school.

Verification / Alternative check:
His net eastward movement is 8 km plus 5 km, totalling 13 km. There is no movement west, so he remains 13 km east of the school. For north south displacement, he moves 6 km north and then 10 km south, giving a net of 4 km south. So from the school as the origin, his final position lies in the South-east quadrant, which confirms the direction as South-east.
Why Other Options Are Wrong:
The option West is incorrect because he clearly has moved net eastward. The option East ignores the fact that he has a net southward component too, so the correct description must mention South-east rather than purely East. The option North-east is not correct because his net vertical displacement is southward, not northward.
Common Pitfalls:
Students often mis-handle the turning instructions, especially when the text says he turns towards a named direction after previously using relative left or right turns. Some also add distances without checking signs, which can produce a mistaken northward displacement. Drawing a simple grid with coordinates helps keep the direction sense accurate.
Final Answer:
The boy is finally located in the South-East direction from his school.

Question 16

Ankita travels 35 km towards the west from her original position, then takes a right turn and travels 50 km, and next she takes another right turn and travels 35 km in that new direction. After completing this path, how far is she now from her origi…

Accepted Answer

Introduction / Context:
In this question Ankita traces a path that forms three sides of a rectangle. We are asked how far she is from the starting point after two right turns and three straight segments. This is another displacement question where the net distance from the origin is different from the total distance travelled. Recognising the rectangular structure simplifies the problem.
Given Data / Assumptions:

Ankita travels 35 km towards the west from the original position.
She then takes a right turn and travels 50 km.
Next she takes another right turn and travels 35 km.
Right turns are 90 degree right angle turns relative to her current direction.
All roads are straight and lie in a horizontal plane.

Concept / Approach:
We again use a coordinate system. Movements west and east affect the horizontal coordinate, while movements north and south affect the vertical coordinate. Because the first and third legs both have length 35 km and run in opposite horizontal directions, those horizontal components will cancel. The remaining displacement will then be along the vertical axis only, which makes the final distance equal to the length of that single vertical leg.
Step-by-Step Solution:
Step 1: Place the starting point at (0, 0). After moving 35 km west, Ankita is at (−35, 0).
Step 2: Facing west, a right turn makes her face north. She then travels 50 km north, reaching (−35, 50).
Step 3: From facing north, a second right turn makes her face east. She travels 35 km east, increasing the horizontal coordinate from −35 to 0, so she reaches (0, 50).
Step 4: The starting position was (0, 0). The final position is (0, 50). Therefore, she is 50 km north of her original position.

Verification / Alternative check:
Observe that her 35 km west movement is exactly countered by a 35 km east movement later, resulting in no net east west displacement. Only the 50 km northward leg remains unbalanced, so her net displacement from the start is just 50 km north. Since the question asks how far she is from the original position, the answer is simply 50 km regardless of direction.
Why Other Options Are Wrong:
The options 75 km, 20 km, and 25 km result from mistaken addition or subtraction of the different legs, such as adding 35 km and 50 km directly or subtracting them in the wrong order. Those calculations fail to recognise that the west and east horizontal legs cancel, leaving only a single vertical leg of 50 km as the net displacement.
Common Pitfalls:
A typical error is to treat the path as a triangle and apply the Pythagoras theorem incorrectly to 35 km and 50 km, or to simply sum some of the distances. Another mistake is to forget that the last leg is in the opposite horizontal direction to the first leg, which leads to ignoring cancellation. Visualising the path as a three sided rectangle makes it easier to see that only one side does not get cancelled.
Final Answer:
Ankita is now 50 km away from her original starting position.

Question 17

Study the following information carefully and answer the given questions.  Five ships (A, B, C, D, and E) are moored at Dock M, and their captains (P, Q, R, S, and T) are steering their respective ships. Each ship starts from the dock, moves in a sp…

Accepted Answer

Concept & Direction Sense
To find the relative direction, determine the final coordinates of each point on a Cartesian plane where the starting dock is the origin (0,0). North is positive y-axis, South is negative y-axis, East is positive x-axis, West is negative x-axis.

Step-by-Step Solution
• Coordinate mapping for R: Ship C moves south 6m (0, -6), turns right (west) and moves 5m (-5, -6), turns left (south) and moves 9m (-5, -15). Final position R = (-5, -15).
• Coordinate mapping for S: Ship D moves west 10m (-10, 0), turns left (south) and moves 4m (-10, -4), turns right (west) and moves 6m (-16, -4). Final position S = (-16, -4).
• Determine relative direction: To go from R to S, we move from x = -5 to x = -16 (West) and from y = -15 to y = -4 (North).
• Since the movement is towards the North and West, S is North-West of R.

Exam Strategy & Shortcut
Instead of drawing the entire complex diagram for all ships, only trace the paths of the specific ships mentioned in the question to save time.

Common Pitfall
Misinterpreting left and right turns when moving South or West. Remember to orient yourself in the direction of travel.

Final Answer
Therefore, the correct answer is North-west.

Question 18

Study the following information carefully and answer the given questions.  Five ships (A, B, C, D, and E) are moored at Dock M, and their captains (P, Q, R, S, and T) are steering their respective ships. Each ship starts from the dock, moves in a sp…

Accepted Answer

Concept & Distance Calculation
The total distance covered by a ship is the simple arithmetic sum of all the individual straight-line segments it travelled, regardless of the direction.

Step-by-Step Solution
• Distance covered by Q (Ship B): It moves 12m, then 7m, then 3m. Total distance = 12 + 7 + 3 = 22	ext{ m}.
• Distance covered by R (Ship C): It moves 6m, then 5m, then 9m. Total distance = 6 + 5 + 9 = 20	ext{ m}.
• Total combined distance: Sum the individual distances: 22	ext{ m} + 20	ext{ m} = 42	ext{ m}.

Exam Strategy & Shortcut
For "total distance covered" (not shortest distance/displacement), simply scan the text for the numbers associated with the specific ships and add them up. You do not need to deduce directions at all.

Common Pitfall
Confusing "total distance" with "shortest distance" (displacement) from the starting point.

Final Answer
Therefore, the correct answer is 42m.

Question 19

Study the following information carefully and answer the given questions.  Five ships (A, B, C, D, and E) are moored at Dock M, and their captains (P, Q, R, S, and T) are steering their respective ships. Each ship starts from the dock, moves in a sp…

Accepted Answer

Concept & Direction Sense
Evaluate each statement by determining the final coordinates of the relevant ships relative to the starting point (0,0). North is positive y-axis, East is positive x-axis.

Step-by-Step Solution
• Map Q (Ship B): East 12m (12, 0), right (south) 7m (12, -7), right (west) 3m (9, -7). Position Q = (9, -7).
• Map T (Ship E): North 8m (0, 8), right (east) 10m (10, 8), right (south) 5m (10, 3). Position T = (10, 3).
• Check statement (c): Compare T to Q. T's x-coordinate (10) is greater than Q's (9), meaning it is further East. T's y-coordinate (3) is greater than Q's (-7), meaning it is further North. Thus, T is North-East of Q. This statement is true.
• Let's briefly verify others: P is (-8, 15), so it is North-West of Q, not North-East.

Exam Strategy & Shortcut
When checking multiple statements, start by evaluating the directional ones (like options a and c) before calculating complex shortest distances, as directional checks are often faster to deduce mentally.

Common Pitfall
Drawing the diagram inaccurately without paying attention to the relative lengths of the segments, leading to wrong visual conclusions about relative positions.

Final Answer
Therefore, the correct answer is T is in north-east of Q.

Question 20

Study the following information carefully and answer the given questions.  Five ships (A, B, C, D, and E) are moored at Dock M, and their captains (P, Q, R, S, and T) are steering their respective ships. Each ship starts from the dock, moves in a sp…

Accepted Answer

Concept & Pythagorean Theorem
The shortest distance between two points on a 2D plane (initial and final position) is calculated using the distance formula or Pythagorean theorem: 	ext{Distance} = \sqrt{\Delta x^2 + \Delta y^2}.

Step-by-Step Solution
• Find initial position: The starting dock is the origin (0, 0).
• Find final position of Ship B (Q): It moves east 12m to (12, 0), turns right (south) 7m to (12, -7), and turns right (west) 3m to (9, -7).
• Calculate shortest distance: The displacement in the x-direction is 9m (East) and in the y-direction is -7m (South).
• Using Pythagoras: 	ext{Distance} = \sqrt{9^2 + (-7)^2} = \sqrt{81 + 49} = \sqrt{130}	ext{ m}.

Exam Strategy & Shortcut
Break the movement into net horizontal and vertical components. Net East = 12 - 3 = 9. Net South = 7. The shortest distance is simply the hypotenuse of a right triangle with legs 9 and 7.

Common Pitfall
Simply adding the segments (12 + 7 + 3) instead of finding the straight-line displacement.

Final Answer
Therefore, the correct answer is \sqrt{130} m.

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