Question 1

From a point Lokesh starts walking towards the south and after walking 30 metres he turns to his right and walks 20 metres, then he turns right again and walks 30 metres and finally he turns to his left and walks 40 metres. In which direction is he …

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Introduction / Context:
Lokesh walks along a path with several right angle turns. The question asks only for his final direction relative to the starting point, not the exact distance. After completing the path, we must understand whether his final position lies north, south, east or west of where he began. This is a classic direction sense problem that can be solved using simple coordinate reasoning.
Given Data / Assumptions:
- Lokesh starts from a point and walks 30 m south.
- He then turns right from facing south and walks 20 m.
- He then turns right again and walks 30 m.
- Finally, he turns left and walks 40 m.
- Directions are standard and each turn is 90 degrees.
Concept / Approach:
We place the starting point at (0, 0), treat south as negative y and west as negative x, and evaluate each movement. The key idea is to determine the net horizontal and vertical displacement at the end of the path. The sign of the horizontal displacement tells us if he is east or west of the start, and the sign of the vertical displacement tells us if he is north or south. In this path, the vertical movements cancel, leaving a purely westward displacement.
Step-by-Step Solution:
1. Start at (0, 0).
2. Walk 30 m south: position becomes (0, -30).
3. Facing south, a right turn points west; walk 20 m west to (-20, -30).
4. From facing west, another right turn points north; walk 30 m north to (-20, 0).
5. From facing north, a left turn points west; walk 40 m west to (-60, 0).
6. Final position is (-60, 0), which is 60 m west of the starting point with no north south displacement.
Verification / Alternative check:
Add vertical legs separately: 30 m south followed by 30 m north results in net 0 vertical movement, so Lokesh ends up on the same east west line as the start. Horizontally, he moves 20 m west and another 40 m west, for a total of 60 m west. A diagram illustrates a rectangle formed by the first three legs, and the final leg extends further west along the same horizontal line. This clearly shows that he is directly west of the origin.
Why Other Options Are Wrong:
- East would require positive x displacement, but Lokesh has only westward movement.
- South would require a negative y displacement at the end, but vertical movement cancels out.
- South East and North West are diagonals, but the final position is purely west, not shifted north or south.
Common Pitfalls:
Mistakes often come from misinterpreting right and left turns when facing different directions. Another issue is forgetting that 30 m north cancels 30 m south. Keeping a small table of cumulative x and y values or drawing the path as segments on a grid makes it much easier to arrive at the correct direction without confusion.
Final Answer:
Lokesh is to the west of the starting point.

Question 2

Five girls Neha, Shalini, Rekha, Neetu and Pooja are sitting in a row facing north. Rekha is between Shalini and Neetu. Pooja is to the immediate right of Neetu and Shalini is to the immediate right of Neha. Who is sitting in the middle position in …

Accepted Answer

Introduction / Context:
This is a seating arrangement question involving five girls sitting in a row facing north. Several relative position conditions are given, and we must determine who occupies the middle seat. Such problems test logical deduction and the ability to translate verbal clues into a consistent ordering.
Given Data / Assumptions:
- The girls are Neha, Shalini, Rekha, Neetu and Pooja.
- All are sitting in a single row facing north.
- Rekha is between Shalini and Neetu.
- Pooja is to the immediate right of Neetu.
- Shalini is to the immediate right of Neha.
- Left and right are taken from the girls' own perspective while facing north (left is to the west, right is to the east).
Concept / Approach:
When everyone faces north, the leftmost seat is at the west end and the rightmost at the east end. We use the "immediate right" relations to form fixed pairs and then incorporate the "between" condition to fit all girls into five seats. By trying possible placements systematically and eliminating contradictions, we find all valid arrangements. The middle girl is then identified from the consistent ordering(s).
Step-by-Step Solution:
1. From "Shalini is to the immediate right of Neha," we get the pair Neha, Shalini in adjacent seats from left to right.
2. From "Pooja is to the immediate right of Neetu," we get the pair Neetu, Pooja in adjacent seats from left to right.
3. Rekha is between Shalini and Neetu, so along the row we must have either Shalini, Rekha, Neetu or Neetu, Rekha, Shalini in that order.
4. Combine these constraints by trial. One valid arrangement is Neetu, Pooja, Rekha, Neha, Shalini, which does not satisfy the adjacency of Neha and Shalini in the correct order.
5. A consistent arrangement that works is Neetu, Pooja, Rekha, Neha, Shalini if we misplace the pair; checking again we see it does not match all conditions.
6. Two correct complete arrangements that satisfy all conditions are: (Neetu, Pooja, Rekha, Neha, Shalini) and (Neha, Shalini, Rekha, Neetu, Pooja) after carefully applying each clue.
7. In both consistent orders, Rekha occupies the central third seat, confirming that the middle position is always held by Rekha.
Verification / Alternative check:
Focus only on relative order segments. Since Rekha is between Shalini and Neetu, the three of them must appear in the order Shalini, Rekha, Neetu or Neetu, Rekha, Shalini. At the same time, Shalini must sit immediately to the right of Neha, and Pooja must sit immediately to the right of Neetu. By building the sequence from left to right and testing both variants, we find that Rekha naturally falls into the third position in any valid 5 seat layout. Drawing the row and filling from the outside inward helps confirm that Rekha must be in the middle seat.
Why Other Options Are Wrong:
- Shalini and Neetu appear towards one end or just next to Rekha depending on the arrangement, but not in the central seat in all consistent cases.
- Pooja must be immediately to the right of Neetu, which places her at an extreme right position in one pattern and not in the middle.
- Neha sits adjacent to Shalini but not at the very center once all constraints are satisfied.
Common Pitfalls:
It is easy to misinterpret "between" as "immediately between" or to forget that immediate right means exactly one seat away, not somewhere to the right. Another common mistake is to settle on one arrangement quickly without checking if all clues are satisfied. Writing all constraints clearly and building the row step by step ensures that the central position is identified correctly.
Final Answer:
The girl sitting in the middle position is Rekha.

Question 3

A man is facing west and turns anticlockwise by 90 degrees and moves 10 m straight, then he again turns 90 degrees anticlockwise. Which direction is the man facing now?

Accepted Answer

Introduction / Context:
This question concerns only the direction in which a man is facing after making two anticlockwise turns of 90 degrees each, starting from facing west. The distance he moves after the first turn does not change his orientation. Such problems assess understanding of rotational directions on the compass and do not require coordinate calculations.
Given Data / Assumptions:
- Initially the man is facing west.
- He turns anticlockwise by 90 degrees and walks 10 m.
- He then again turns 90 degrees anticlockwise.
- All turns are right angle turns and there are no further movements after the second turn.
Concept / Approach:
Anticlockwise rotation on the compass moves from north to west, west to south, south to east and east to north. Starting from a given direction, each 90 degree anticlockwise turn simply shifts to the next direction in this sequence. The distance walked after the first turn does not change direction, so we only apply the rotations to deduce the final orientation. Counting these rotations carefully produces the correct answer quickly.
Step-by-Step Solution:
1. Initial direction: west.
2. First anticlockwise 90 degree turn from west moves him to face south.
3. He then walks 10 m while facing south, but his facing direction remains south.
4. Second anticlockwise 90 degree turn from south moves him to face east.
5. After this second turn, there is no additional movement mentioned, so his final facing direction is east.
Verification / Alternative check:
We can visualize this using a compass diagram: north at the top, east to the right, south at the bottom and west to the left. Place an arrow pointing left (west). Rotating it anticlockwise once points it downwards (south). Rotating it anticlockwise a second time points it to the right (east). This visual check immediately confirms the orientation without involving the 10 m movement at all.
Why Other Options Are Wrong:
- North would require three anticlockwise turns from west or equivalent rotation, which is not given.
- West is the initial direction; two anticlockwise rotations cannot bring him back to west.
- South is only the intermediate direction after the first turn, not the direction after the second turn.
- North East is a diagonal direction that never appears in a sequence of right angle turns among cardinal directions.
Common Pitfalls:
Some learners confuse clockwise with anticlockwise rotation or mistakenly think in terms of their own left and right when observing from outside. It is important to fix the compass in mind and rotate consistently in the requested direction. Ignoring the unnecessary distance moved and focusing only on the sequence of turns helps avoid distraction and errors.
Final Answer:
After the two anticlockwise turns, the man is facing east.

Question 4

A courier delivery person starts from a fixed point and rides 6 km towards the south, then turns towards the west and rides 2 km, then turns to his right and rides 6 km, and finally turns again towards the west and rides 8 km. With respect to his st…

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Introduction / Context:This problem belongs to the standard direction sense category in verbal reasoning. Such questions test whether a student can mentally track movements on the ground using cardinal directions and turns, and then convert that mental path into a final relative position from the starting point. These questions are very common in bank exams, SSC, railway exams and other competitive tests, so mastering the basic technique is very helpful.Given Data / Assumptions:The courier rider starts from an initial reference point which we call the origin.He first cycles 6 km towards the south.He then turns towards the west and cycles 2 km.After that he turns to his right, which from west means towards the north, and cycles 6 km.Finally he turns again towards the west and cycles 8 km more.We assume all segments are straight line paths and directions are perfect cardinal directions.Concept / Approach:The most reliable method is to imagine or sketch a simple coordinate system. We treat the starting point as (0, 0). Movement towards the north increases the y coordinate, movement towards the south decreases it. Movement towards the east increases the x coordinate and movement towards the west decreases it. After plotting every leg of the journey, we compare the final coordinates with the origin and read off how far and in which direction the courier has moved from the start.Step-by-Step Solution:Step 1: Place the courier at the origin, which we mark as (0, 0).Step 2: He rides 6 km south. South means the y coordinate decreases. New position becomes (0, -6).Step 3: From there he turns towards the west and rides 2 km. West means x decreases. New position becomes (-2, -6).Step 4: At this point he turns to his right. When someone is facing west, a right turn means facing north. Riding 6 km north increases the y coordinate by 6. Position becomes (-2, 0).Step 5: Finally he turns again towards the west and rides 8 km. Moving 8 km west decreases the x coordinate by 8. The final position becomes (-10, 0).Step 6: The starting point was (0, 0). The final point is (-10, 0). This means he is 10 km away along the west direction from the starting point.Verification / Alternative check:We can also check without coordinates by grouping vertical and horizontal movements separately. In the vertical direction, he goes 6 km south and later 6 km north, so these cancel each other out, bringing him back to the same north south level as the start. In the horizontal direction he moves 2 km west and later 8 km more west, which gives a total of 10 km west. Since there is no eastward movement to balance this, he must finish 10 km west of the origin. This confirms our coordinate based result.Why Other Options Are Wrong:Option B (6 km West) ignores the final extra 8 km west movement and treats only the first horizontal leg. Option C (10 km East) reverses the correct direction, confusing west with east. Option D (6 km East) is inconsistent with every leg of the path, because there is no eastward motion at all in the description. Only the option that places him 10 km to the west of his starting point matches the net displacement.Common Pitfalls:Students often make mistakes when interpreting a right turn from a given facing direction. Right from west is north, not south. Another frequent error is to add distances without considering sign and cancellation. For example, some may simply add all numbers and misinterpret 6, 2, 6, and 8 as a single linear distance. The safe approach is always to separate horizontal and vertical components and ensure that movements in opposite directions are netted properly. Drawing a quick rough diagram on paper helps many aspirants avoid confusion.Final Answer:The courier delivery person ends up 10 km to the west of his starting position, so the correct option is “10 km West”.

Question 5

A man walks 3 km towards the west, then turns towards the south and walks 7 km, then turns towards the east and walks 3 km, and finally turns to his right and walks 5 km. Where is he now with respect to his original starting position?

Accepted Answer

Introduction / Context:This is a classic direction sense problem in which a person walks in several straight line segments, changing direction at right angles. The objective is to track the path and determine the final position in terms of both distance and direction from the starting point. Questions of this type train spatial reasoning skills and are widely used in competitive examinations to test basic logical and geometric understanding without requiring any advanced mathematics.Given Data / Assumptions:The man starts from a fixed starting point.He first walks 3 km towards the west.He then turns towards the south and walks 7 km.After that he turns towards the east and walks 3 km.Finally he turns to his right and walks 5 km.All turns are right angle turns and the ground is assumed to be flat and level.Concept / Approach:We use a simple coordinate geometry idea. Take the starting point as (0, 0). West movement means decreasing the x coordinate, east movement means increasing it. North means increasing the y coordinate and south means decreasing it. When the man turns, we carefully note his new facing direction before handling the next segment. At the end, the difference between the final coordinates and the origin gives the net displacement, which we then convert back into plain language as distance and direction from the starting point.Step-by-Step Solution:Step 1: Start from the origin, represented as (0, 0).Step 2: The man walks 3 km west, so the x coordinate decreases by 3 and the new position is (-3, 0).Step 3: He now faces west. Turning towards the south means he faces downward on our diagram. Walking 7 km south decreases the y coordinate, so the position becomes (-3, -7).Step 4: From this point he turns towards the east. Moving 3 km east increases the x coordinate by 3, giving a new position of (0, -7).Step 5: At (0, -7), he is facing east. A right turn from east means he now faces south again. Walking 5 km south decreases the y coordinate by another 5, leading to a final position of (0, -12).Step 6: Comparing with the starting point (0, 0), his x coordinate is unchanged and the y coordinate is -12. Therefore he is 12 km to the south of his starting point.Verification / Alternative check:Instead of coordinates, we can summarise the vertical and horizontal movements. Horizontally, he first walks 3 km west and later 3 km east, so these cancel each other and he has no net east west displacement. Vertically, he walks a total of 7 km south first and later another 5 km south, making a total of 12 km south. Since there is no northward movement, the overall displacement is directly 12 km south from the origin. This cross check matches the coordinate method and confirms the result.Why Other Options Are Wrong:Option A (12 km North) reverses the correct direction, confusing south with north. Option B (2 km South) incorrectly subtracts some distances and does not follow the complete path. Option D (2 km North) is inconsistent because there is no northward movement in any step. Only option C correctly captures both the magnitude and the direction: 12 km away from the starting point towards the south.Common Pitfalls:Many candidates forget to adjust the concept of left and right according to the current facing direction of the walker. Another common mistake is to add all distances in a straight manner and ignore cancellation. Using a rough sketch or simple coordinate representation helps to avoid these errors. Always account for each turn and remember that movements in opposite directions can cancel out when considering net displacement.Final Answer:The man is finally located 12 km to the south of his starting point, so the correct option is “12 km South”.

Question 6

From point A, Ram first moves 100 m towards the north east, then turns and walks 100 m towards the south east, then turns again and walks 100 m towards the south west, and finally moves 100 m towards the north west. With respect to point A, where is…

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Introduction / Context:This direction sense question is based on movements along four diagonal directions: north east, south east, south west and north west. The pattern of directions suggests that the person is tracing out a closed geometric figure, and the task is to identify the final position relative to the starting point. Understanding symmetry and cancelling of movements is crucial here, and this type of reasoning appears frequently in aptitude tests to check visualisation skills.Given Data / Assumptions:Ram starts from a fixed point labelled A.He walks 100 m in the north east direction.Next he walks 100 m in the south east direction.Then he walks 100 m in the south west direction.Finally he walks 100 m in the north west direction.All diagonal directions are at 45 degrees to the cardinal axes and all distances are equal straight line segments.Concept / Approach:Each diagonal direction can be split into a pair of perpendicular components, one north south and one east west. For example, north east contains equal parts north and east, while south west contains equal parts south and west. Because all segments have the same length, their horizontal and vertical components can cancel neatly. The key insight is that moving once in each of the four diagonal directions with equal distance creates a closed loop and brings the person back to the starting point, similar to walking around a square or diamond shape.Step-by-Step Solution:Step 1: Consider the first move of 100 m towards north east. This can be thought of as some amount north and the same amount east.Step 2: The second move is 100 m towards south east. This has the same east component as the first move but a south component equal in magnitude to the previous north component.Step 3: After these two moves, the north and south components cancel each other, leaving only an effective movement towards the east.Step 4: The third move is 100 m towards south west. This adds a west component and a south component which begin to cancel out the remaining east and the upcoming north west movement.Step 5: The final move of 100 m in the north west direction has equal north and west components, effectively cancelling the residual south and east components from the earlier legs.Step 6: Because the distances and diagonal angles are symmetric, the total north south displacement and the total east west displacement both become zero. Therefore, Ram returns to the original starting point A.Verification / Alternative check:A simple way to visualise this is to imagine a square or a rhombus. Starting from one corner, moving 100 m north east, then 100 m south east, then 100 m south west, and finally 100 m north west corresponds to moving all around the four sides of a closed figure and coming back to the starting corner. This geometric picture provides a quick mental verification without explicit component calculations.Why Other Options Are Wrong:Options A (West) and D (East) suggest that there is a net horizontal shift, which would only happen if the diagonal moves were not balanced. Option B (Southwest) implies a net diagonal movement, again ignoring the symmetry. Only option C correctly states that Ram is at point A, meaning his net displacement is zero after completing the four moves of equal length and symmetric directions.Common Pitfalls:Candidates often treat diagonal moves as if they were purely horizontal or vertical, which leads to incorrect cumulative results. Another mistake is to stop tracking after two or three moves, without noticing that the fourth move completes the loop. When diagonal directions appear in a symmetric pattern with equal distances, it is usually a hint that the path closes back on itself. Keeping an eye on symmetry is a powerful shortcut in many direction sense problems.Final Answer:After completing all four diagonal movements, Ram returns to his starting point, so he is exactly at point A and not displaced in any direction.

Question 7

Two motorcycle riders, A and B, start from the same point. Rider A rides 11 km towards the east and then turns to his right and rides another 9 km. Rider B rides 8 km towards the north, then turns towards the east and rides 11 km, and finally turns …

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Introduction / Context:This question asks about the relative position of two moving objects, both starting from the same point but following different routes. It checks whether the student can track two paths simultaneously and then compare their final positions. Such problems combine the basic direction sense technique with relative displacement, which is a very common pattern in reasoning sections of competitive exams.Given Data / Assumptions:Rider A starts from the common origin and goes 11 km east.Then rider A turns to his right and travels 9 km.Rider B also starts from the same origin and goes 8 km north.Rider B then turns east and travels 11 km.Finally, rider B turns to his right and travels 7 km.All paths are straight and all turns are at right angles.Concept / Approach:We use a simple coordinate based approach. Place the common starting point at (0, 0). East is taken as positive x, west as negative x, north as positive y and south as negative y. Calculate the final coordinates of rider A and rider B separately. Once we have both positions, we subtract to find the displacement of A relative to B, which tells us in which direction and how far A is from B.Step-by-Step Solution:Step 1: For rider A, start at (0, 0). Move 11 km east to (11, 0).Step 2: Facing east, a right turn means facing south. Riding 9 km south changes the position to (11, -9).Step 3: For rider B, begin at the same origin (0, 0). Move 8 km north, reaching (0, 8).Step 4: From there, B turns east and rides 11 km, which moves him to (11, 8).Step 5: B now faces east. A right turn from east means facing south. Travelling 7 km south gives B the final position (11, 1).Step 6: Rider A is at (11, -9) and rider B is at (11, 1). The x coordinates are equal, so both are on the same vertical line. The y coordinate of A is 10 units less than that of B, meaning A is 10 km south of B.Verification / Alternative check:We can ignore the first common segment in the east direction for both riders, because ultimately they both shift to the same east coordinate of 11 km. The difference lies only in how far north or south they end up. From the starting point, B effectively goes 8 km north and then 7 km south, ending 1 km north of the origin. A goes no north at all but ends 9 km south. Therefore, A is 10 km south of B, which agrees with the coordinate method and confirms that the calculation is consistent.Why Other Options Are Wrong:Option B (8 km South) mistakenly focuses on a partial difference in north south travel. Option C (10 km North) reverses the correct direction. Option D (8 km North) again selects the wrong magnitude and direction. Only option A captures both the correct distance and the correct orientation by stating that rider A is 10 km to the south of rider B.Common Pitfalls:Candidates may mix the paths of the two riders or forget that both share the same starting point. Another typical error is to compare each leg individually instead of the final net displacement. Keeping the paths separate, assigning coordinates, and then comparing final positions is the safest and most general method for all such relative position questions.Final Answer:Rider A is located 10 km to the south of rider B, so the correct option is “10 km South”.

Question 8

A plane flies 100 km towards the west, then turns towards the south and flies 150 km, then turns again towards the west and flies 300 km, and finally turns to its right and flies 150 km. Where is the plane now with reference to its starting position?

Accepted Answer

Introduction / Context:This question is another example of a multi step direction sense problem, but using a plane instead of a person. The distances are larger, yet the underlying reasoning is the same. We need to track movements along cardinal directions, account for turns, and finally express the net displacement from the origin in a simple direction and distance form. These skills are widely tested in reasoning sections where spatial tracking is important.Given Data / Assumptions:The plane starts from a fixed reference point.First it flies 100 km towards the west.Then it turns towards the south and flies 150 km.Next it turns towards the west again and flies 300 km.Finally it turns to its right and flies 150 km.The earth is treated locally as flat, with movements arranged as straight segments and turns of ninety degrees.Concept / Approach:We use the coordinate method that is standard for direction sense problems. The starting point is taken as (0, 0). West corresponds to negative x, east to positive x, north to positive y and south to negative y. We compute the plane's coordinates after each leg of the journey and then compare the final coordinates with the origin. Since the last move is back towards the north, some vertical displacement cancels out, and we only need to keep track of what remains horizontally and vertically.Step-by-Step Solution:Step 1: Start with the plane at (0, 0).Step 2: It flies 100 km west, so the new position is (-100, 0).Step 3: It then turns south and flies 150 km, which makes the position (-100, -150).Step 4: The plane now turns west again and flies 300 km more. This moves it to (-400, -150).Step 5: Finally, it turns to its right. When facing west, a right turn leads to facing north. Flying 150 km north takes the plane from (-400, -150) to (-400, 0).Step 6: The starting point was (0, 0) while the final point is (-400, 0). Therefore, the plane is 400 km to the west of its starting position and at the same north south level.Verification / Alternative check:We can separate horizontal and vertical components. Horizontally, the plane moves 100 km west first and 300 km west later, which gives a total of 400 km west. There is no eastward movement at any stage. Vertically, it flies 150 km south and later 150 km north, so the vertical displacement is zero. Thus the net displacement is purely horizontal: 400 km to the west. This quick summary confirms the coordinate result and rules out any error in sign or cancellation.Why Other Options Are Wrong:Option B (200 km West) underestimates the total horizontal movement by combining only a part of the path. Options A and D (400 km East and 200 km East) reverse the direction, which contradicts the repeated westward flights. Only option C correctly states that the plane ends up 400 km west of the starting point, which matches the resultant displacement from our calculation.Common Pitfalls:One frequent error is to forget that the final northward movement cancels the earlier southward movement. Candidates sometimes add all distances linearly without recognising direction changes, which leads to an incorrect combined distance. Another pitfall comes from misinterpreting the final right turn from west, sometimes assumed to lead south instead of north. A small sketch with labelled arrows helps avoid these confusions.Final Answer:The plane is finally positioned 400 km to the west of its starting point, so the correct option is “400 km West”.

Question 9

L, M, N, O and P are standing in a straight line facing east. N is standing at the north end of the line and O is standing at the south end. L and M are standing together, and P is a neighbour of both M and N. Who is standing third from the north en…

Accepted Answer

Introduction / Context:This is a basic linear arrangement question combined with directional labels for the two ends of the line. The participants are placed in a straight line, and the task is to use the given adjacency and end position conditions to determine the exact order and then identify who is third from the north end. Such arrangement questions are common in reasoning tests and reward careful use of constraints rather than guesswork.Given Data / Assumptions:Five people L, M, N, O and P are standing in a line facing east.N is standing at the north end of the line.O is standing at the south end of the line.L and M are together, meaning they stand in consecutive positions.P is a neighbour of both M and N.The positions are arranged from north end at the top to south end at the bottom.Concept / Approach:We treat the line as a vertical arrangement with positions numbered from 1 (north end) to 5 (south end). N must occupy the first position and O must occupy the fifth position. The conditions that L and M sit together and that P is neighbour of both M and N severely limit the possible placements. We systematically test positions consistent with all clues and then read off who sits in the required position counting from the north end.Step-by-Step Solution:Step 1: Since N is at the north end, N must be in position 1.Step 2: Since O is at the south end, O must be in position 5.Step 3: P is neighbour of N, which is in position 1, so P must be in position 2 because that is the only adjacent position.Step 4: P is also neighbour of M. If P is in position 2, M must occupy position 3, the only remaining position adjacent to position 2.Step 5: L and M must be together. With M already fixed at position 3, L must be in position 4 in order to be adjacent to M.Step 6: The complete order from north end to south end is now N, P, M, L, O. Counting from the north end, the third position is occupied by M.Verification / Alternative check:Once the arrangement N, P, M, L, O is found, we can quickly verify all statements. N is at the north end and O at the south end. L and M are in consecutive positions (3 and 4). P is adjacent to both N and M because it stands between them in position 2. No other arrangement satisfies all conditions at once, so this order is unique and confirms that M is indeed third from the north end.Why Other Options Are Wrong:Option A (L) corresponds to the fourth position from the north, not the third. Option B (O) is at the south end, which is position five. Option D (P) is in the second position from the north. Only option C correctly matches the person in the third position from the north end, namely M.Common Pitfalls:A typical mistake is to misinterpret the phrases north end and south end as directions facing rather than as labels for the ends of the line. Another error occurs when students try to place L and M first and later attempt to adjust the arrangement, which can violate the requirement that P must be neighbour of both M and N. A clean approach is always to place the end points first, apply the neighbour conditions step by step and only then check remaining positions.Final Answer:The person standing third from the north end is M, so the correct option is “M”.

Question 10

X and Y start from the same point. X walks 40 m towards the north, then turns towards the west and walks 80 m, and then turns to his right and walks 50 m. At the same time, Y walks 90 m towards the north in a straight line. Where is Y now with respe…

Accepted Answer

Introduction / Context:This problem combines direction sense with relative positioning of two people who start together but follow different routes. Such questions are highly relevant for exams because they test a candidate's ability to simultaneously track more than one path and then compare their final positions diagrammatically or numerically. Learning a systematic approach reduces the chance of confusion when several turns and distances are involved.Given Data / Assumptions:X and Y both start from the same initial point.X walks 40 m towards the north.Then X turns towards the west and walks 80 m.Next X turns to his right and walks 50 m.During this time, Y walks straight 90 m towards the north from the starting point.All paths are straight and turns are right angles.Concept / Approach:We set up a coordinate system with the starting point as (0, 0). We then track the movement of each person separately. For X we account for the three legs with turns. For Y we account for a single straight path towards the north. Once we have final coordinates for both, the relative position of Y with respect to X is simply the vector difference between these coordinates, which translates into a descriptive answer like 80 m east of X.Step-by-Step Solution:Step 1: Start both X and Y at the origin (0, 0).Step 2: For X, move 40 m north to reach (0, 40).Step 3: From there X turns west and moves 80 m, giving position (-80, 40).Step 4: X is now facing west. A right turn from west means facing north. Moving 50 m north changes the y coordinate to 90, so X reaches (-80, 90).Step 5: For Y, from the origin (0, 0), moving 90 m north directly leads to the position (0, 90).Step 6: Now we compare X at (-80, 90) and Y at (0, 90). Both have the same y coordinate 90, so they are on the same east west line. The x coordinates differ by 80 units, with Y at 0 and X at -80. Therefore, Y is 80 m to the east of X.Verification / Alternative check:We can visualise the situation by noting that X and Y end up at the same north south level, both having travelled a total of 90 m north in different stages. However, X also travels 80 m west that is never counterbalanced by any eastward movement. Y does not move west or east at all. So relative to X, Y must be 80 m east. This geometric reasoning matches the coordinate computation and confirms the answer.Why Other Options Are Wrong:Options A and C that mention 30 m east or west are incorrect because they are based on a mistaken difference in north south displacement rather than horizontal distance. Option B (80 m west) reverses the direction, placing Y incorrectly to the west of X. Only option D correctly states that Y is 80 m east of X, capturing both magnitude and direction properly.Common Pitfalls:Students sometimes compare each leg of movement individually rather than the final positions, which can lead to mixing up distances. Another pitfall is misinterpreting the right turn from west, which must give north, not south. Keeping a small sketch and marking the intermediate points reduces such errors. Always compute or sketch the final coordinates and then compare rather than making a judgment midway.Final Answer:Y is located 80 m to the east of X, so the correct option is “Y is 80 m to the East of X”.

Question 11

A man walks 20 m towards the north, then turns to his right and walks 3 m, then turns left and walks 4 m, and from there walks another 4 m towards the east. How far is he from his initial position, and in which direction from the starting point is h…

Accepted Answer

Introduction / Context:This problem is slightly different from simple direction sense questions because it asks for both distance and direction from the starting point after several turns and movements. To answer correctly, we must treat the displacements as sides of a right angled triangle and then apply the Pythagoras theorem to compute the straight line distance between the start and end positions. These questions develop a candidate's ability to combine geometry with direction sense reasoning.Given Data / Assumptions:The man starts from an initial position.He walks 20 m towards the north.He then turns right and walks 3 m.Next, he turns left and walks 4 m.From that point, he walks 4 m towards the east.All paths are straight and all turns are right angle turns.Concept / Approach:We again use a coordinate system with the origin as the starting point. We convert every movement into a change in x or y coordinate. Once we find the final coordinates, we use the formula distance = square root of (x^2 + y^2) to calculate how far the man is from the origin. The direction is then inferred by observing the signs of the x and y coordinates, which tell us the quadrant in which the final point lies, such as north east.Step-by-Step Solution:Step 1: Start at (0, 0). The man first walks 20 m north to reach (0, 20).Step 2: From north, a right turn leads to facing east. Walking 3 m east changes the position to (3, 20).Step 3: He now faces east. A left turn from east makes him face north again. Walking 4 m north moves him to (3, 24).Step 4: From (3, 24), the problem says he walks 4 m towards the east, which leads to the final position (7, 24).Step 5: The net horizontal displacement from the origin is 7 m to the east (x = 7) and the net vertical displacement is 24 m to the north (y = 24).Step 6: The distance from the origin is given by the length of the hypotenuse of a right angled triangle: distance = square root of (7^2 + 24^2) = square root of (49 + 576) = square root of 625 = 25 m.Step 7: Since both x and y are positive, the man is in the north east direction from the starting point.Verification / Alternative check:We can quickly recognise the famous Pythagorean triple 7, 24, 25. The legs of the triangle are 7 m and 24 m and the hypotenuse is 25 m, which confirms the calculation. A mental diagram with the starting point, intermediate turns and final point also clearly shows that the end point lies diagonally to the north east of the origin, not directly north or east.Why Other Options Are Wrong:Option A (25 m East) has the correct distance but wrong direction, ignoring the significant 24 m northward component. Option C (20 m North) confuses the first leg of the journey with the total displacement. Option D (24 m North) uses the vertical component only and omits the horizontal component. Only option B correctly combines both distance and quadrant by stating 25 m in the north east direction from the starting point.Common Pitfalls:A common mistake is to add all distances numerically rather than treating them as perpendicular components. Another frequent error is to misinterpret right and left turns when the orientation changes multiple times. The safest method is to maintain a small coordinate system or diagram and to mark each movement in sequence, then apply Pythagoras theorem for the final displacement when both x and y components are non zero.Final Answer:The man is finally located 25 m away from his starting point in the north east direction, so the correct option is “25 m North-East”.

Question 12

A boy and a girl are facing each other. If the boy is standing to the north west of the girl, then in which direction is the girl located with respect to the boy?

Accepted Answer

Introduction / Context:This question is a simple relative direction problem. Instead of moving along a path, we compare the positions of two people directly. The phrase that one person is at the north west of another immediately implies the reverse relation by symmetry. Such questions are usually straightforward and are meant to check whether the candidate can mentally reverse directions without confusion.Given Data / Assumptions:A boy and a girl are standing in such a way that they are facing each other.The boy is at the north west of the girl.We are asked for the direction of the girl with respect to the boy, not with respect to any external reference point.North west and south east are diagonal directions midway between the main cardinal directions.Concept / Approach:When we say that point B is at the north west of point G, it means that if we stand at G and move north and west simultaneously, we will reach B. In coordinate terms, B has a greater north component and a more westward component compared with G. The reverse relation from B to G is obtained by taking the opposite direction along both axes. The opposite of north is south and the opposite of west is east. Hence, from the boy's point of view, the girl must be to the south east.Step-by-Step Solution:Step 1: Imagine the girl at some point G on the ground.Step 2: The boy is at point B, which is to the north west of G. That means B lies up and to the left of G in a standard north up, east right diagram.Step 3: Now consider the direction from B back to G. To reach G from B, we must go downwards (south) and to the right (east).Step 4: Combining these two opposite directions gives the diagonal direction south east.Step 5: Therefore, with respect to the boy, the girl is located in the south east direction.Verification / Alternative check:This can be verified by thinking of a compass rose. North west and south east are opposite each other on the compass, forming a straight line through the centre. If one person is at north west relative to the other, the second person must be exactly at south east relative to the first. This symmetry property holds for other opposite pairs as well, such as north and south or north east and south west.Why Other Options Are Wrong:Option A (North) would be correct if the girl were directly south of the boy or if the given statement were reversed. Option B (South) ignores the east west component. Option C (East) takes only one component of the required direction. Only option D, south east, correctly combines south (opposite of north) and east (opposite of west) as required for the reverse relation.Common Pitfalls:Students sometimes mistakenly assume that if one person is north west of another, then the other is south west or north east, mixing up which axis to invert. The safe rule is that to reverse the relation, each component of the direction must be replaced by its exact opposite: north with south, east with west. When both components are changed, north west automatically becomes south east and vice versa.Final Answer:With respect to the boy, the girl is located in the south east direction, so the correct option is “South-East”.

Question 13

A boy travels 4 km towards the south and then takes a right turn and travels another 3 km in that new direction. How far is he now from his original position and in which direction from the starting point is he located?

Accepted Answer

Introduction / Context:This is a basic two step direction sense question where the final displacement forms a right angled triangle. The goal is to compute both the distance from the origin and the approximate direction of the final point. Such questions often rely on recognising simple Pythagorean triples and understanding that combining south and west displacements yields a south west resultant direction.Given Data / Assumptions:The boy starts from a fixed initial position.He travels 4 km towards the south.He then takes a right turn and travels 3 km.Taking a right turn while initially facing south means he then travels towards the west.We assume straight paths and exact right angle turns.Concept / Approach:We place the starting point at (0, 0). Moving south decreases the y coordinate, and moving west decreases the x coordinate. After computing the final coordinates, we view the displacement vector as the hypotenuse of a right angled triangle whose legs are 3 km and 4 km. The length of this hypotenuse gives the straight line distance from the starting point, and the signs of the coordinates tell us that the direction lies in the south west quadrant.Step-by-Step Solution:Step 1: Start with coordinates (0, 0).Step 2: Moving 4 km south leads to the point (0, -4).Step 3: While facing south, a right turn leads to facing west. Travelling 3 km west changes the coordinates to (-3, -4).Step 4: The net displacement is therefore 3 km west and 4 km south from the origin.Step 5: The distance from the origin is the hypotenuse of a right angled triangle with sides 3 and 4, so distance = square root of (3^2 + 4^2) = square root of (9 + 16) = square root of 25 = 5 km.Step 6: Since both x and y coordinates are negative, the position is to the south west of the starting point.Verification / Alternative check:The numbers 3, 4 and 5 form a very common Pythagorean triple that appears in many reasoning and quantitative aptitude questions. Knowing this triple allows a quick mental check that the straight line distance must be 5 km when the perpendicular movements are 3 km and 4 km. A small sketch with a vertical line of 4 km downward and a horizontal line of 3 km to the left clearly shows a diagonal pointing to the south west direction.Why Other Options Are Wrong:Option A (6 km, south) incorrectly adds distances and ignores the westward movement. Option C (4 km, north) not only chooses the wrong distance but also the opposite vertical direction. Option D (5 km, north-west) has the correct distance but the wrong quadrant, because the movements were south and west, not north and west. Only option B, 5 km towards the south west, correctly represents the net displacement.Common Pitfalls:Students sometimes misinterpret the right turn when facing south, mistakenly thinking it leads to east rather than west. Another mistake is to treat 3 km and 4 km as distances along the same straight line and simply add them. Remember that when two moves are perpendicular, you should form a triangle and use the Pythagoras theorem to compute net displacement.Final Answer:The boy is finally 5 km away from his starting position in the south west direction, so the correct option is “5 km, south-west”.

Question 14

A person A travels 12 km towards the north, then takes a left turn and covers another 5 km. From that point, he turns 180 degrees anticlockwise and travels 10 km further in the new direction. What is the minimum straight line distance between his in…

Accepted Answer

Introduction / Context:This is a direction sense question where we must determine the shortest straight line distance between the starting and final positions after a series of moves and a 180 degree anticlockwise turn. Unlike problems that only ask for the direction, here we must also calculate the distance, which again uses basic right angled triangle geometry combined with coordinate tracking.Given Data / Assumptions:A travels 12 km towards the north from the starting point.He then turns left and travels 5 km.From there he turns 180 degrees anticlockwise and then travels another 10 km.All moves are along straight lines and the initial directions follow standard north south and east west axes.Turning 180 degrees anticlockwise simply reverses his current direction, regardless of clockwise or anticlockwise.Concept / Approach:We once again use a coordinate system. North is positive y, east is positive x. We will update the coordinates after each segment. The interesting part is interpreting the 180 degree anticlockwise turn correctly: it points the traveler in the exact opposite direction to the one he was facing just before that turn. Once we have the final coordinates, we apply the Pythagoras theorem to get the straight line distance from the origin.Step-by-Step Solution:Step 1: Place the starting point at (0, 0).Step 2: A travels 12 km north, so his position becomes (0, 12).Step 3: Facing north, a left turn means facing west. Moving 5 km west brings him to (-5, 12).Step 4: He is now facing west. A 180 degree anticlockwise turn reverses his direction, so he ends up facing east.Step 5: From (-5, 12), moving 10 km east increases the x coordinate by 10, giving a final position of (5, 12).Step 6: The net displacement from the origin is 5 km east and 12 km north, which forms a right angled triangle with legs 5 and 12.Step 7: Using the Pythagoras theorem, distance = square root of (5^2 + 12^2) = square root of (25 + 144) = square root of 169 = 13 km.Verification / Alternative check:The numbers 5, 12 and 13 form a very common Pythagorean triple. Whenever the perpendicular displacements are 5 and 12, the shortest distance between the start and end points is 13. Sketching the path clearly shows a rectangle like shape where the final point is diagonally offset from the origin by 5 units horizontally and 12 units vertically. This quick geometric insight confirms the algebraic computation.Why Other Options Are Wrong:Option A (8 km) and Option C (6 km) underestimate the distance by either incorrectly adding or subtracting legs without forming a right angled triangle. Option D (12 km) only counts the first vertical movement and ignores the horizontal and later movements. Only option B correctly matches the length of the hypotenuse of the right angled triangle formed by 5 km and 12 km, giving 13 km as the minimum distance between start and end points.Common Pitfalls:Some candidates misunderstand a 180 degree anticlockwise turn and treat it differently from a 180 degree clockwise turn, even though both point in exactly the opposite direction. Another common mistake is to attempt to simply sum or subtract distances when multiple perpendicular directions are involved. The robust method is to treat perpendicular moves as components of a vector and then use the Pythagoras theorem to find the straight line distance.Final Answer:The minimum straight line distance between the initial and final positions of A is 13 km, so option “13 km” is correct.

Question 15

A, B, C, D and E are standing in a line facing north. E is standing 40 metres to the left of B. A is standing 20 metres to the left of C. D is standing 20 metres to the right of E and 50 metres to the right of C. With respect to D, where is B standi…

Accepted Answer

Introduction / Context:This problem deals with a linear arrangement on a number line measured in metres, with everyone facing north. Instead of discrete seats, the positions are given as distances to the left or right of each other. The task is to translate the verbal geometric descriptions into coordinates on a line and then determine the relative position of one person with respect to another. Questions like this test algebraic thinking and spatial interpretation together.Given Data / Assumptions:The five people A, B, C, D and E stand on a straight line facing north.E is 40 metres to the left of B.A is 20 metres to the left of C.D is 20 metres to the right of E.D is also 50 metres to the right of C.Left and right are measured from the perspective of a person facing north, so left corresponds to west and right to east on a horizontal number line.Concept / Approach:We model the line as a one dimensional axis. Let us assume a coordinate for B and then derive coordinates for E, D, C and A using the given distances. Once we establish a consistent set of positions, the relative location of B with respect to D is simply the difference of their coordinates. This approach helps avoid confusion that sometimes arises from manipulating left and right statements directly in words.Step-by-Step Solution:Step 1: Assume B stands at coordinate 0 for convenience.Step 2: E is 40 metres to the left of B, so E stands at coordinate -40.Step 3: D is 20 metres to the right of E, so D stands at -40 + 20 = -20.Step 4: D is also 50 metres to the right of C. Therefore, C must stand at coordinate -20 - 50 = -70.Step 5: A is 20 metres to the left of C, so A stands at -70 - 20 = -90.Step 6: We now have consistent positions: A at -90, C at -70, E at -40, D at -20, and B at 0.Step 7: The question asks for the position of B with respect to D. Since D is at -20 and B at 0, B is 20 metres to the right (east) of D.Verification / Alternative check:We can cross check the relations. E is indeed 40 metres left of B because -40 is 40 units less than 0. D is 20 metres right of E since -20 is 20 units greater than -40. D is 50 metres right of C because -20 is 50 units greater than -70. A is 20 metres left of C since -90 is 20 units less than -70. All conditions are satisfied, so the coordinate assignment is correct and the derived relation between B and D is reliable.Why Other Options Are Wrong:Option B (30 metres right) and Option C (40 metres right) overstate the distance between B and D. Option D (40 metres left) reverses the direction and also changes the magnitude. A gap of exactly 20 metres separates D and B in the eastward direction, so only option A correctly states that B stands 20 metres to the right of D.Common Pitfalls:Students often get confused switching between left right descriptions from different reference persons. A robust way is to fix one coordinate system and stick to it, treating all positions relative to a chosen origin. Another pitfall is misreading phrases like right of C or left of B as right of D, which leads to inconsistent distances. Working carefully through each relationship and drawing a number line can help avoid these errors.Final Answer:B is standing 20 metres to the right of D, therefore the correct option is “20 metres right”.

Question 16

Anitha walks 20 km towards the north, then turns right and walks 30 km, then turns right again and travels 35 km, then moves left and walks 15 km, and finally turns left once more and walks 15 km. In which direction is she from her starting point at…

Accepted Answer

Introduction / Context:This direction sense problem involves several segments with changes in direction at right angles. The question focuses on the final direction of Anitha relative to her starting point rather than the exact distance. This tests whether a student can keep track of the north south and east west components separately and see how some movements cancel while others accumulate, leaving a net direction.Given Data / Assumptions:Anitha first walks 20 km north.She then turns right and walks 30 km.She turns right again and travels 35 km.She moves left and walks 15 km.Finally, she turns left again and walks 15 km.All movements take place on flat ground with right angle turns, and directions follow the usual compass orientation.Concept / Approach:We represent the starting point as (0, 0). North increases the y coordinate, south decreases it, east increases the x coordinate and west decreases it. At each turn we update Anitha's facing direction and apply the next movement accordingly. After all segments, we compare the final coordinates with the origin and determine which cardinal direction best describes her position relative to the starting point.Step-by-Step Solution:Step 1: Start at (0, 0). Walking 20 km north takes Anitha to (0, 20).Step 2: From facing north, a right turn leads to facing east. Walking 30 km east changes her position to (30, 20).Step 3: From facing east, another right turn makes her face south. Travelling 35 km south moves her to (30, 20 - 35) = (30, -15).Step 4: From facing south, a left turn leads to facing east. Walking 15 km east changes the position to (45, -15).Step 5: From facing east, another left turn leads to facing north. Walking 15 km north moves her to (45, 0).Step 6: The final coordinates are (45, 0). The starting point was (0, 0). Therefore, Anitha is 45 km to the east of her starting point and at the same north south level.Verification / Alternative check:We can separately track north south and east west components. Total northward distance is 20 km from the first leg plus 15 km from the last leg, giving 35 km north. Total southward distance is 35 km. Thus the vertical components cancel completely, leaving no net north south displacement. For the horizontal direction, she walks 30 km east and then another 15 km east, with no westward leg, so the net horizontal displacement is 45 km east. Consequently, her final direction relative to the starting point is purely east.Why Other Options Are Wrong:Option A (South) would be correct only if southward movements exceeded northward ones. Option B (North) would require a net positive vertical displacement, which is not the case because north and south distances balance. Option D (West) reverses the actual direction of horizontal displacement. Only option C, east, correctly reflects the fact that the net movement is entirely eastward from the starting point.Common Pitfalls:One common error is losing track of the current facing direction after multiple turns, especially left and right chains. Another is neglecting to cancel opposite movements in the same axis. Drawing a simple schematic or using plus and minus signs for north south and east west distances helps maintain clarity. Candidates should practise a few similar problems to make this systematic approach automatic.Final Answer:At the end of the described journey, Anitha is to the east of her starting point, so the correct option is “East”.

Question 17

A person goes 5 km towards the east, then turns right and goes 8 km, then turns left and goes 5 km, and finally turns left again and goes 8 km. After completing this path, what is his distance from the starting point?

Accepted Answer

Introduction / Context:Here we have a direction sense question where the person traces a kind of rectangle, but the distances on the sides are not symmetric around the starting point. Instead of simply returning to the start, the person ends up at a point horizontally displaced from the origin. The problem asks for the straight line distance between the starting and ending points, which uses coordinate tracking and the Pythagoras theorem.Given Data / Assumptions:The person walks 5 km east from the starting point.He then turns right and walks 8 km, which means he now travels towards the south.Next, he turns left and walks 5 km, which makes him travel towards the east again.Finally, he turns left once more and walks 8 km, which makes him travel towards the north.All movements are straight, and turns are ninety degree turns.Concept / Approach:We use coordinates with origin at the starting point. By updating x and y for each leg of the journey, we obtain the final coordinates. Because the vertical distances turn out to cancel fully, the net displacement lies entirely along the east west direction, and the distance is simply the absolute difference in x coordinates. The process demonstrates how rectangular paths can still yield non zero displacement when the side lengths are unequal around the start.Step-by-Step Solution:Step 1: Start at (0, 0).Step 2: Move 5 km east to reach (5, 0).Step 3: Facing east, a right turn leads to facing south. Walking 8 km south moves him to (5, -8).Step 4: From facing south, a left turn leads to facing east again. Walking 5 km east takes him to (10, -8).Step 5: From facing east, another left turn makes him face north. Walking 8 km north brings him to the final position (10, 0).Step 6: The starting point was (0, 0) and the final point is (10, 0), which means there is no vertical displacement and a net 10 km displacement towards the east.Verification / Alternative check:If we consider vertical movements only, the person moves 8 km south and later 8 km north, which cancel each other. For horizontal movement, he first travels 5 km east and later another 5 km east, giving a total of 10 km east without any westward movement. Therefore, his final position is 10 km east of the starting point. Since there is no north south offset, the straight line distance between the two points is exactly 10 km.Why Other Options Are Wrong:Option A (8 km) confuses the vertical leg with the net displacement. Option B (0 km) would be correct only if he returned to the starting point, which he does not. Option D (5 km) again reflects only one part of the total horizontal distance. Only option C correctly states that the person ends up 10 km from the starting point.Common Pitfalls:Candidates may mistakenly assume that whenever a rectangular path is traced, the person must return to the starting point, overlooking the possibility that the starting corner and ending corner can be different. Another pitfall is mismanaging left and right turns when the direction changes from east to south and so on. Drawing a rectangle and carefully marking the lengths and directions is often enough to see the displacement clearly.Final Answer:The person is finally located 10 km away from his starting point, so the correct option is “10 km”.

Question 18

Vishal travels 8 km towards the east, then turns left and travels another 5 km, and finally turns 270 degrees anticlockwise from his current facing direction. In which cardinal direction is he facing now?

Accepted Answer

Introduction / Context:This problem focuses purely on turning directions rather than positions. After making some moves, Vishal makes a 270 degree anticlockwise turn, and we are asked to find his final facing direction. Understanding how to interpret clockwise and anticlockwise rotations around the compass is essential for many direction sense and reasoning questions.Given Data / Assumptions:Vishal first travels 8 km towards the east.He then turns left and travels 5 km, which makes him face north during that second leg.From that north facing orientation, he turns 270 degrees anticlockwise.The distance covered after the final turn is not given and is not needed, as the question asks only for the facing direction.Concept / Approach:We track only Vishal's orientation. Starting from east, a left turn is equivalent to a 90 degree anticlockwise rotation, placing him facing north. From north, a 270 degree anticlockwise rotation can be thought of as three successive left turns or a single right turn (90 degrees clockwise), because rotating anticlockwise by 270 degrees is the same as rotating clockwise by 90 degrees. We can use either interpretation to determine the final direction.Step-by-Step Solution:Step 1: Initially Vishal is facing east during his first 8 km of travel.Step 2: He then turns left. A left turn from east means turning 90 degrees anticlockwise to face north.Step 3: Now he faces north. From this orientation, he makes a 270 degree anticlockwise turn.Step 4: A convenient way to think about a 270 degree anticlockwise turn is that it equals three successive 90 degree anticlockwise turns.Step 5: From north, one 90 degree anticlockwise turn leads to west, the second leads to south, and the third leads to east.Step 6: Thus, after the full 270 degree anticlockwise turn, Vishal will be facing east.Verification / Alternative check:We can also treat a 270 degree anticlockwise rotation as a 90 degree clockwise rotation, since both complete a full 360 degrees when combined. From north, a 90 degree clockwise turn clearly leads to east. This alternative reasoning confirms that east is the correct final facing direction.Why Other Options Are Wrong:Option A (West) corresponds to a 90 degree anticlockwise turn from north, not 270 degrees. Option C (North) would be the direction if Vishal did not rotate at all. Option D (South) corresponds to a 180 degree turn. Hence, only option B matches the required 270 degree anticlockwise rotation, giving east as the final facing direction.Common Pitfalls:Candidates often confuse 270 degrees anticlockwise with 270 degrees clockwise or misinterpret it as 90 degrees in the opposite sense. A useful strategy is to remember that turning anticlockwise by 270 degrees is equivalent to turning clockwise by 90 degrees. Drawing a simple compass and marking each 90 degree turn is another quick method to avoid confusion.Final Answer:After completing the described turns, Vishal is facing east, so the correct option is “East”.

Question 19

Navjot starts moving towards the west. After covering some distance he turns left, and after walking in that new direction he takes a right turn. After these turns, in which direction is he facing now?

Accepted Answer

Introduction / Context:This is a pure turning direction question without any distances or final position calculation. It tests whether the student correctly understands how left and right turns change orientation when the initial facing direction is not north. Such questions are simple but often cause mistakes if candidates try to visualise turns without a clear mental compass.Given Data / Assumptions:Navjot starts by moving towards the west.He then turns left and walks some distance.After that he takes a right turn and walks again.The exact distances covered after each turn are not relevant; only the directions of facing matter.Concept / Approach:We focus solely on orientation changes. When facing west, the left side is towards the south and the right side is towards the north. From the new south facing orientation, we interpret a right turn as a rotation towards the west. Tracking these two turns in sequence lets us deduce Navjot's final facing direction, independent of how far he travels along each leg.Step-by-Step Solution:Step 1: Initially Navjot is facing west.Step 2: From west, a left turn means turning towards the south because the left side of someone facing west points south.Step 3: He then walks in that southward direction for some distance.Step 4: Now he is facing south. From south, a right turn means turning towards the west.Step 5: Therefore, after the left and right turns, Navjot is again facing west.Verification / Alternative check:Another way to see this is to imagine a person standing on a sheet of paper labelled with the four cardinal directions. Mark an arrow pointing towards west, then rotate it 90 degrees anticlockwise to point towards south, and then rotate it 90 degrees clockwise to return it to west. The final orientation matches the original one, confirming that the sequence left then right from west leads back to west.Why Other Options Are Wrong:Option A (South) would be the direction if Navjot stopped after the first left turn and did not take the subsequent right turn. Option B (North) never occurs in the sequence of turns described. Option D (East) is the opposite of the initial direction and would require two left or two right turns from west in succession. The only correct option that matches the actual final facing direction is West.Common Pitfalls:Students sometimes imagine left and right turns relative to a fixed north rather than relative to the person's current orientation, which leads to incorrect answers. A good habit is to mentally stand in the given direction yourself and then simulate turning left or right from that orientation. Doing this for each turn step by step avoids mixing up directions.Final Answer:After starting towards the west, turning left, and then turning right, Navjot finally faces west, so the correct option is “West”.

Question 20

A cat is chasing a mouse. The cat first moves 25 m towards the north, then takes a right turn and moves 100 m, then turns towards the south and moves 25 m further, and finally turns left and moves 55 m. What is the straight line distance between the…

Accepted Answer

Introduction / Context:This is a path based direction question that ends with a request for the straight line distance between the starting and ending positions. The cat moves along a rectangular path with an additional horizontal leg at the end. Identifying the net displacement and calculating the direct distance between the two extreme points is the central task, which is typical of direction sense questions that also require basic numerical calculation.Given Data / Assumptions:The cat starts from an initial point.It moves 25 m north.It then takes a right turn from that north facing direction and moves 100 m, which means it moves east.Next, it turns towards the south and moves 25 m.Finally, it turns left from the south facing direction and moves 55 m, which means it moves east again.All motions are along straight segments with right angle turns.Concept / Approach:We use the coordinate framework. Let the starting point be (0, 0). We track each move as changes in x and y coordinates. After the north and south legs, we check whether the vertical displacement cancels. After the eastward legs, we sum the horizontal displacement. The net displacement forms a straight horizontal segment, and the distance between the initial and final positions is simply the absolute horizontal difference because the vertical component turns out to be zero.Step-by-Step Solution:Step 1: Start at (0, 0). After moving 25 m north, the cat is at (0, 25).Step 2: Facing north, a right turn means facing east. Moving 100 m east shifts the position to (100, 25).Step 3: The cat then turns south and moves 25 m, reducing the y coordinate back to 0 and arriving at (100, 0).Step 4: Now it faces south. A left turn from south means facing east. Moving 55 m east changes the position to (155, 0).Step 5: The starting point is (0, 0) and the final point is (155, 0). The vertical coordinate is the same in both, so there is no north south displacement and the net displacement is purely eastward.Step 6: Therefore, the straight line distance between the initial and final positions is 155 m.Verification / Alternative check:Track vertical and horizontal movements separately. Vertically, the cat goes 25 m north and later 25 m south, which exactly cancel. Horizontally, it goes 100 m east first and later 55 m east again, so total eastward movement is 155 m. With no westward leg at any stage, the final position must be 155 m east of the starting point. This logic matches the coordinate calculation and confirms our answer.Why Other Options Are Wrong:Option A (185 m) and Option C (190 m) are larger than the actual net eastward displacement and likely come from adding extra segments incorrectly. Option D (135 m) underestimates the distance, possibly by dropping one of the horizontal legs. Only option B correctly gives 155 m as the straight line separation between start and end points.Common Pitfalls:Many students forget that the north and south movements cancel exactly and incorrectly include them in the final distance calculation. Another error is misinterpreting the left turn from south, which must lead to east, not west. Drawing a simple diagram with all four legs marked clearly helps in seeing the final layout as a horizontal line between two points separated by 155 m.Final Answer:The distance between the initial and final positions of the cat is 155 m, so the correct option is “155 m”.

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