Question 1

Afreena walks 8 km towards the East and then walks 13 km back along the same line. She then turns left and walks 4 km, turns left again and walks 5 km, and finally turns left once more and walks 3 km. How far is she from her starting point?

Accepted Answer

Introduction: This direction–sense question describes Afreena walking forwards, then backtracking past her starting point, and then making a series of left turns. We must compute her final straight-line distance from the starting point. By treating the path as a sequence of movements on a coordinate plane and carefully tracking each turn, we can determine the final displacement and hence the distance. Given Data / Assumptions: • Afreena walks 8 km towards the East.• Then she walks 13 km back along the same line (towards the West).• She then turns left and walks 4 km.• Then turns left again and walks 5 km.• Finally, she turns left once more and walks 3 km.• We assume she always turns relative to the direction in which she is currently walking. Concept / Approach: We model Afreena's movements using coordinates: East as positive x, West as negative x, North as positive y and South as negative y. Each segment changes her position and, when a turn occurs, also changes her facing direction. By updating coordinates step by step, we can find where she ends up relative to the origin representing her starting point and compute the straight-line distance between these two points. Step-by-Step Solution: Step 1: Place the starting point at (0, 0) and let Afreena face East initially. Walking 8 km East takes her to (8, 0).Step 2: She then walks 13 km back along the same line, which means towards the West. From x = 8, moving 13 km West gives x = 8 − 13 = −5. Her position is now (−5, 0) and she is facing West.Step 3: From facing West, a left turn points South. Walking 4 km South takes her to (−5, −4).Step 4: From facing South, another left turn makes her face East. Walking 5 km East from (−5, −4) moves her to (0, −4).Step 5: From facing East, a further left turn makes her face North. Walking 3 km North from (0, −4) moves her to (0, −1).Step 6: Her final position is (0, −1), while her starting point is (0, 0).Step 7: The distance between (0, 0) and (0, −1) is simply 1 km, since the x-coordinate is unchanged and the y-coordinate differs by 1. Verification / Alternative check: Summarising the net movements: along the East–West axis she has 8 km East and 13 km West, giving a net 5 km West followed by 5 km East, which cancel to 0. So she ends with no net East–West displacement. Along the North–South axis she has 4 km South and 3 km North, giving a net 1 km South. Thus, she is 1 km to the South of her starting point, confirming the distance of 1 km. Why Other Options Are Wrong: Distances like 2 km, 3 km, 5 km or 6 km would require a greater imbalance in the final coordinates, which is not supported by the step-by-step calculation. Those values might arise if you forget one of the turns or mis-handle the backtracking of 13 km. Only 1 km is consistent with both the coordinate approach and the net displacement summary. Common Pitfalls: It is easy to forget that walking 13 km back from a position 8 km East of the start will carry Afreena 5 km to the West of the starting point. Some learners also misinterpret left turns when facing West or South. Drawing the path roughly to scale can help make it clear that the final point lies almost but not exactly above the origin, at a distance of 1 km. Final Answer: Afreena is finally 1 km away from her starting point.

Question 2

Hemant, in order to go to the university, starts from his house which is located in the East of a road crossing. He comes to the crossing, where the road to the left leads to a theatre and the road straight ahead leads to a hospital. In which direct…

Accepted Answer

Introduction: This is a conceptual direction–sense problem about a road junction and the relative position of different destinations. Hemant starts from a house located in the East of a crossing and walks towards the crossing. We are told where the theatre and hospital lie with respect to Hemant's route at the crossing, and we must infer the likely direction of the university, which is the remaining road at the junction. Given Data / Assumptions: • Hemant's house is in the East of a crossing.• He walks from his house to the crossing, so he walks from East towards the West.• At the crossing, the road to the left leads to a theatre.• The road straight ahead leads to a hospital.• The university is on another road from the same crossing. Concept / Approach: When Hemant reaches the crossing, his facing direction is the same as the direction he walked in to reach it. Since his house is in the East, he must be walking West. At the crossing, the road straight ahead is therefore towards the West, and the road to his left is towards the South. The fourth road (the one not mentioned) must then be towards the North. That remaining direction is where the university lies. Step-by-Step Solution: Step 1: Place the crossing at the centre of a simple compass diagram.Step 2: Hemant's house is to the East of the crossing. To get from his house to the crossing, he must walk West.Step 3: When he reaches the crossing, he is therefore facing West.Step 4: The road straight ahead for him at that point is in the West direction, and we are told that this road leads to the hospital.Step 5: When a man faces West, his left-hand side is towards the South. Thus, the road to his left is towards the South and leads to the theatre.Step 6: The remaining directions at the crossing are East (behind him) and North (to his right). The road behind is where he came from and not where the university is said to be.Step 7: Therefore, the only remaining unused direction for another destination is North. Hence, the university must be in the North direction from the crossing. Verification / Alternative check: If we imagine standing at the crossing facing West, the four roads are clearly arranged as: West straight ahead, East behind, South to the left, and North to the right. We already know which roads lead to the theatre and hospital. The unexplained road must be the one to the right (North), which is the natural candidate for the university in this type of puzzle. Why Other Options Are Wrong: South is already associated with the theatre. East is where Hemant's house is located and corresponds to the road behind him. West is associated with the hospital. Therefore, these directions are already taken. Only North remains unused and must be the direction of the university. Common Pitfalls: Some students mistakenly reverse Hemant's direction and assume he is walking East towards the crossing, which flips left and right and leads to incorrect conclusions. Another frequent error is to ignore "from his house in the East" and assume he is standing at the crossing facing North. Always base left and right on the direction of travel described in the problem. Final Answer: From the crossing, the university is located towards the North direction.

Question 3

The length and breadth of a rectangular room are 8 m and 6 m respectively. A cat runs once along all four walls of the room (around the perimeter) and finally runs along one of the diagonals to catch a rat. What is the total distance covered by the …

Accepted Answer

Introduction: This is a distance and geometry problem presented in a direction–sense context. We are told the dimensions of a rectangular room and that a cat runs around the four walls (the perimeter) and then along a diagonal of the room. The task is to compute the total distance travelled by the cat, which involves both perimeter and diagonal calculations for a rectangle. Given Data / Assumptions: • The room is rectangular with length 8 m and breadth 6 m.• The cat runs along all four walls, meaning along the entire perimeter once.• Then the cat runs along a diagonal of the room.• We assume the room is perfectly rectangular and that the diagonal connects two opposite corners. Concept / Approach: The total distance is the sum of the perimeter of the rectangle and the length of one diagonal. For a rectangle with length L and breadth B, the perimeter is 2 * (L + B). The diagonal can be found using the Pythagorean theorem because the diagonal, length and breadth form a right-angled triangle. Specifically, diagonal = sqrt(L^2 + B^2). Once we compute these two quantities, adding them gives the required total distance. Step-by-Step Solution: Step 1: Compute the perimeter of the room. With length L = 8 m and breadth B = 6 m, the perimeter P is:P = 2 * (L + B) = 2 * (8 + 6) = 2 * 14 = 28 m.Step 2: Compute the diagonal using the Pythagorean theorem:Diagonal = sqrt(L^2 + B^2) = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 m.Step 3: Add the perimeter distance and the diagonal distance to get the total distance the cat covers:Total distance = perimeter + diagonal = 28 + 10 = 38 m. Verification / Alternative check: We can check our calculations by observing that 8–6–10 is a well-known Pythagorean triplet similar to the classic 3–4–5 triangle, just scaled up by a factor of 2. Therefore, a rectangle with sides 8 and 6 must indeed have a diagonal of 10 m. The perimeter formula 2 * (8 + 6) is straightforward, so the arithmetic is reliable. Hence, 38 m is confidently the correct total distance. Why Other Options Are Wrong: The diagonal alone is 10 m, so 10 cannot be the total distance because the cat also runs along the walls. The perimeter alone is 28 m, so 34 and 14 are also too small or incorrectly derived. A value of 48 m would correspond to adding another 10 m or miscalculating the perimeter, perhaps as 38 m, but correct calculations do not support this. Only 38 m fits the correct sum of perimeter and diagonal. Common Pitfalls: Some students misread "runs along all the four walls" as running twice around the perimeter or only along two adjacent walls. Others incorrectly calculate the diagonal using L + B or some other non-Pythagorean expression. Remember that diagonals in rectangles always use the formula sqrt(L^2 + B^2), and that one full lap along four walls is simply the perimeter. Final Answer: The cat covers a total distance of 38 metres.

Question 4

Ravi wants to go to the university. He starts from his home, which is situated in the East of a crossing, and walks to the crossing. There, the road to his left leads to a theatre and the road straight ahead leads to a hospital. In which direction i…

Accepted Answer

Introduction: This question is structurally identical to the earlier Hemant example and tests the same reasoning: interpreting a person's facing direction at a road crossing and then deducing which directions the various roads represent. Ravi starts from the East, walks to a crossing, and we know where the theatre and hospital are. We must identify the remaining direction, which is where the university lies. Given Data / Assumptions: • Ravi's home is in the East of a crossing.• He walks from his home to the crossing, so he travels West.• At the crossing, the road to his left leads to a theatre.• The road straight ahead leads to a hospital.• The university is at one of the remaining directions from the crossing. Concept / Approach: When Ravi reaches the crossing, his facing direction is the same as the direction in which he has been walking, namely West. We then interpret "left" and "straight ahead" using this facing direction. The road behind him is East, where he came from. The road to his left, when facing West, is South. The road straight ahead is West. The only unused direction then is North, where the university must be located. Step-by-Step Solution: Step 1: Place the crossing at the origin of a compass diagram.Step 2: Since Ravi's home is in the East, his journey from home to the crossing is along the West direction, so he arrives at the crossing facing West.Step 3: The road straight ahead of him (in the direction he is facing) is thus the West road. According to the problem, this road leads to the hospital.Step 4: When a person faces West, the left-hand side is towards the South. So the road to his left is the South road, and this one leads to the theatre.Step 5: The road behind him is the East road, returning to his home, and is not mentioned as leading to the university.Step 6: The only remaining direction from the crossing is the North road. Therefore, the university must be to the North of the crossing. Verification / Alternative check: If you sketch the situation with a simple cross-shaped junction and arrows for Ravi's path, you will see that when he approaches from the East, he must be facing West at the junction. It is easy then to label the left as South and straight ahead as West, leaving North as the only unassigned direction for the university. Why Other Options Are Wrong: South is given as the direction to the theatre, not the university. West is the direction to the hospital. East is just the way back home. South-West is a diagonal direction not even considered in the problem statement and cannot represent a road in a simple four-way crossing. Hence they are all unsuitable. Common Pitfalls: A typical mistake is to assume Ravi is initially facing North when he arrives at the crossing, which mislabels his left and straight-ahead routes. Another error is to ignore the phrase "from his home which is in the East" and treat East as just a label rather than part of his path. Always anchor left and right to the person's actual facing direction as they arrive at the crossing. Final Answer: From the crossing, the university lies towards the North direction.

Question 5

A child walked 90 m towards the East to look for his father, then turned right and walked 20 m. After this, he turned right again and, after walking 30 m, reached his uncle's house. Not finding his father there, he walked 100 m towards the North and…

Accepted Answer

Introduction: This problem describes a series of movements by a child who first walks East, then makes two right turns to reach his uncle's house, and finally walks North to meet his father. We are asked to find the straight-line distance from the starting point to the place where he meets his father. A coordinate geometry approach makes it straightforward to track his movements and compute the final distance. Given Data / Assumptions: • The child first walks 90 m towards the East.• He then turns right and walks 20 m.• He turns right again and walks 30 m to reach his uncle's house.• From his uncle's house, he walks 100 m towards the North and meets his father.• We assume level ground and usual interpretations of right turn and cardinal directions. Concept / Approach: We treat his path as movement on an x–y coordinate grid, with East as positive x, West as negative x, North as positive y and South as negative y. Each right turn is a 90 degree clockwise rotation from his current facing direction. By updating both position and facing direction, we can compute his final coordinates relative to the starting point. The straight-line distance is then found using the Pythagorean theorem. Step-by-Step Solution: Step 1: Place the starting point at (0, 0) with the child initially facing East. Walking 90 m East moves him to (90, 0).Step 2: From East, a right turn makes him face South. Walking 20 m South takes him to (90, −20).Step 3: From South, another right turn makes him face West. Walking 30 m West from (90, −20) moves him to (60, −20). This is his uncle's house.Step 4: From the uncle's house, he walks 100 m towards the North. That increases the y-coordinate from −20 to −20 + 100 = 80. His final position is (60, 80).Step 5: To find the distance from the starting point (0, 0) to (60, 80), use the Pythagorean theorem:Distance = sqrt(60^2 + 80^2) = sqrt(3600 + 6400) = sqrt(10000) = 100 m. Verification / Alternative check: Notice that (60, 80) is a scaled version of the classic 3–4–5 right triangle, with sides in the ratio 3:4:5 multiplied by 20. Here 60 = 3 * 20, 80 = 4 * 20, and the hypotenuse 100 = 5 * 20, confirming that the distance must be 100 m. This again matches our coordinate calculation and reinforces that no arithmetic mistake was made. Why Other Options Are Wrong: Distances such as 80 m or 140 m might appear if someone incorrectly added distances in a straight line or misapplied the Pythagorean theorem. A value like 260 m would correspond to summing all path segments, but the question asks for the straight-line distance from the starting point to the meeting point, not the total distance walked. Only 100 m is consistent with the correct geometry. Common Pitfalls: Students sometimes forget that repeated right turns change the facing direction, or they accidentally treat North as positive x instead of positive y when setting up coordinates. Others add all path distances rather than computing the resultant displacement. Drawing a quick sketch and labelling the coordinates at each key point is an excellent way to avoid these errors. Final Answer: The child meets his father at a point that is 100 m away from his starting point.

Question 6

Laxmi goes 6 km towards the south east from her office, then walks 15 km towards the west, after that she goes 6 km towards the north west and finally she walks 11 km towards the east. In this multi step journey, how far is she from her office at th…

Accepted Answer

Introduction / Context: This question is from the direction sense test topic and involves a person moving in several different directions, including diagonal directions such as south east and north west. The aim is to determine the straight line distance from the starting point, which is Laxmi's office, after she completes all the movements. Problems like this check understanding of basic coordinate ideas and vector addition without requiring heavy mathematics. Given Data / Assumptions: Laxmi starts from her office and first walks 6 km towards the south east. Next, she walks 15 km towards the west. Then she walks 6 km towards the north west. Finally, she walks 11 km towards the east. We assume standard directions with east as positive x axis and north as positive y axis, and diagonal directions at 45 degrees. Concept / Approach: The core concept is to resolve each movement into horizontal (east west) and vertical (north south) components and then add them. South east and north west are at 45 degrees, so the horizontal and vertical components of those displacements are equal in magnitude. When two diagonal movements of the same length occur in opposite diagonal directions, many components cancel out, which often simplifies the calculation. We then combine all east west movements and all north south movements to get the net displacement from the office. Step-by-Step Solution: Step 1: Place the office at the origin (0, 0) of a coordinate system with east positive x and north positive y.Step 2: A 6 km south east move has components 6 / √2 km east and 6 / √2 km south. Call 6 / √2 = a.Step 3: After this move, Laxmi is at (a, −a).Step 4: She then walks 15 km west, which subtracts 15 from the x coordinate, giving (a − 15, −a).Step 5: The next 6 km north west move has components a west and a north, so adding (−a, a) gives the new position (a − 15 − a, −a + a) = (−15, 0).Step 6: Finally, she walks 11 km east, which adds 11 to the x coordinate, placing her at (−15 + 11, 0) = (−4, 0).Step 7: The point (−4, 0) is 4 km to the west of the office, so the straight line distance from the office is 4 km. Verification / Alternative check: An intuitive check is to notice that the two 6 km diagonal moves cancel each other in both north south and east west components. The south east move takes her some amount east and the same amount south, while the north west move brings her back by the same amount west and north. This leaves only the pure horizontal movements of 15 km west and 11 km east, which combine to a net 4 km towards the west. Since no north south displacement remains, the distance is exactly 4 km, matching the coordinate calculation. Why Other Options Are Wrong: Options 10 km and 11 km would require a much larger net displacement, which is inconsistent because most of the long legs cancel each other. The option 6 km might be chosen by simply subtracting 15 and 11 without noticing the diagonal cancellation, or by guessing based on one of the step lengths. The option 8 km is another rough guess that does not correspond to any correct Pythagorean combination arising from the data. Only 4 km matches the precise net horizontal displacement from the office. Common Pitfalls: A common mistake is to try to treat diagonal distances as if they were purely horizontal or purely vertical, which leads to incorrect totals. Another frequent error is to add distances algebraically without considering direction, for example adding 6 + 15 + 6 + 11 and then trying to guess the result. Not drawing even a simple rough diagram makes it easy to lose track of the cancelling movements. Thinking in terms of components along east west and north south axes helps keep the logic clear and avoids arithmetic confusion. Final Answer: After completing all the given movements, Laxmi is located 4 km away from her office, towards the west, so the required distance is 4 km.

Question 7

Arun and Amit start walking from two different points A and B respectively. Arun walks 2 km towards the north, then 3 km towards the east, again 4 km towards the north and finally 5 km towards the east to reach point C. Similarly, Amit starts from B…

Accepted Answer

Introduction / Context: This question involves two people starting from different points and walking along different paths to meet at a common point. The topic belongs to direction sense and basic coordinate geometry in verbal reasoning. The main goal is to reconstruct their paths in a simple coordinate system and calculate the distance between their original starting points. It tests the ability to convert word descriptions into a clear diagram or set of coordinates. Given Data / Assumptions: Arun starts from point A. Arun walks 2 km north, 3 km east, 4 km north, and 5 km east to reach point C. Amit starts from point B. Amit walks 2 km north, 3 km west, and 4 km north to reach the same point C. All directions are along standard north south and east west axes, and there is no diagonal movement. Concept / Approach: We can treat the paths as movements on a grid. By placing point A at the origin of a coordinate system, we can find the coordinates of point C using Arun's path. Then we use Amit's path in reverse to determine where point B must be located so that Amit also ends at C. Once we have coordinates for both A and B, the distance between them can be determined by simple horizontal separation, because they lie on the same east west line in this setup. Step-by-Step Solution: Step 1: Place point A at (0, 0) in a coordinate plane with east as positive x and north as positive y.Step 2: Track Arun's movement. After 2 km north he is at (0, 2). After 3 km east he is at (3, 2). After another 4 km north he is at (3, 6). After 5 km east he reaches point C at (8, 6).Step 3: Let Amit start at point B with coordinates (x, y). After 2 km north he is at (x, y + 2). After 3 km west he is at (x − 3, y + 2). After 4 km north he reaches C at (x − 3, y + 6).Step 4: Since both reach the same point C, we equate the coordinates: x − 3 = 8 and y + 6 = 6.Step 5: Solving, we get x = 11 and y = 0, so B is at (11, 0), while A is at (0, 0).Step 6: The distance between A and B is simply the horizontal separation, which is 11 km. Verification / Alternative check: We can verify by running Amit's path explicitly from (11, 0). After 2 km north he reaches (11, 2). After 3 km west he reaches (8, 2). After 4 km north he reaches (8, 6), which matches the coordinate of point C obtained from Arun's path. Because both meet at the same coordinate and the separation between A and B is a straight horizontal segment of length 11, the answer is confirmed as 11 km. Why Other Options Are Wrong: The option 5 km is far too small compared to the size of the grid and does not match any calculated separation. The options 8 km and 7 km might be guessed from partial movements but do not satisfy the coordinate equations. The option 13 km is a common Pythagorean triple value, but here the separation is purely horizontal with no vertical difference, so 13 km is not appropriate. Only 11 km matches the derived coordinates of the two starting points. Common Pitfalls: One common error is to ignore the fact that Arun and Amit meet at the same point and instead treat their paths independently, making it hard to set up correct equations. Another mistake is mixing up east and west movements when writing coordinates, which reverses signs and leads to wrong distances. Drawing a rough diagram or setting up a coordinate table avoids confusion and makes the logic of the problem much clearer. Final Answer: The distance between Arun's starting point A and Amit's starting point B is a straight line segment of length 11 km along the east west direction.

Question 8

A girl is initially facing north. She first rotates through an angle of 100 degrees in the clockwise direction and then rotates through 190 degrees in the anticlockwise direction. After performing both these rotations, in which cardinal direction is…

Accepted Answer

Introduction / Context: This direction sense problem focuses on rotation through given angles and asks for the final facing direction. The starting direction is north, and the girl rotates clockwise and then anticlockwise through specific angles. Such questions test the understanding of clockwise versus anticlockwise rotation and how to combine angle measures to find a net change in direction. Given Data / Assumptions: The girl starts by facing north. She rotates 100 degrees clockwise. Then she rotates 190 degrees anticlockwise. We consider a full circle as 360 degrees with north, east, south, and west at right angle intervals. Clockwise rotation is taken as a negative change and anticlockwise as a positive change when combining angles. Concept / Approach: The key idea is to calculate the net rotation. Instead of tracking every intermediate orientation in detail, we can treat clockwise rotation as negative and anticlockwise as positive and simply add the angles. The resulting net angle tells us how far from the initial direction the person has turned. Once we know the net angle relative to north, we map that angle to a cardinal direction such as east, south, west, or an intermediate direction. Step-by-Step Solution: Step 1: Start with the initial direction as north.Step 2: The first rotation is 100 degrees clockwise, which we treat as −100 degrees.Step 3: The second rotation is 190 degrees anticlockwise, which we treat as +190 degrees.Step 4: Add the rotations to get the net change in direction: −100 + 190 = +90 degrees.Step 5: A net change of +90 degrees anticlockwise from north means we rotate from north through west, because 90 degrees anticlockwise from north lands at west.Step 6: Therefore, after both rotations, the girl is facing west. Verification / Alternative check: We can also track intermediate directions more explicitly. Starting facing north, a 100 degree clockwise turn moves her 90 degrees to east and then 10 degrees further, so she ends up slightly south of east. From there, turning 190 degrees anticlockwise carries her through north (100 degrees), then to west (190 degrees total), which leaves her exactly facing west. This stepwise reasoning matches the net angle method and confirms that west is the correct final direction. Why Other Options Are Wrong: North east and south east would correspond to net rotations of 45 or 315 degrees, which do not match the calculated net 90 degree change. South would correspond to a 180 degree shift from north and also does not fit the 90 degree net rotation. North west requires a 270 degree anticlockwise rotation, which again is inconsistent with the computed net change. Only west aligns with a net 90 degree anticlockwise rotation from the initial north facing position. Common Pitfalls: Learners sometimes incorrectly add both angles as if they were in the same direction, giving 290 degrees, and then try to map that directly to a direction. Another mistake is to confuse clockwise with anticlockwise and subtract in the wrong order. It is safer to assign signs to the rotations and then add them algebraically, or to draw a simple diagram with the four main directions and track each rotation step by step. Final Answer: After rotating 100 degrees clockwise and then 190 degrees anticlockwise, the girl ends up facing towards the West.

Question 9

A traveller first goes 20 miles towards the north, then 25 miles towards the east. After that, he travels 40 miles by turning to his right, then 30 miles by turning to his left, then another 12 miles to his left and finally 20 miles towards the nort…

Accepted Answer

Introduction / Context: This is a multi step direction sense problem where a person travels in several straight segments, turning right or left at different stages. The objective is to find the approximate straight line distance from the starting point and the overall direction of the final position. Questions like this simulate real life navigation and require systematic tracking of horizontal and vertical movements using simple geometry. Given Data / Assumptions: The traveller starts at an initial point which we take as the origin. He moves 20 miles north, then 25 miles east. From facing east, a right turn takes him south, and he travels 40 miles. From facing south, a left turn takes him east, and he travels 30 miles. From facing east, a left turn takes him north, and he travels 12 miles. Finally he travels another 20 miles north in the same direction. Concept / Approach: We treat the movements along east west and north south axes and use coordinates to represent his position after each leg of the journey. Right and left turns are interpreted relative to the direction he is currently facing. Once all displacements are recorded, we add up all east west components and all north south components to get the net displacement vector. The straight line distance is then found using the Pythagorean theorem, and the direction is described by comparing the net east and north components. Step-by-Step Solution: Step 1: Place the starting point at (0, 0) with east as positive x and north as positive y.Step 2: After 20 miles north, his position is (0, 20).Step 3: After 25 miles east, his position is (25, 20), and he is facing east.Step 4: A right turn from east means he now faces south. Travelling 40 miles south takes him to (25, −20).Step 5: A left turn from south means he faces east. Travelling 30 miles east takes him to (55, −20).Step 6: A left turn from east means he faces north. Travelling 12 miles north takes him to (55, −8).Step 7: Finally, travelling another 20 miles north brings him to (55, 12).Step 8: The net displacement from the origin is therefore 55 miles east and 12 miles north.Step 9: The straight line distance d is given by d = √(55^2 + 12^2) = √(3025 + 144) = √3169, which is approximately 56 miles. Verification / Alternative check: We can roughly estimate the distance without exact squares by noting that 55^2 is 3025 and 12^2 is 144, so the sum is slightly above 3000. The square root of 3136 is 56, and 3169 is very close to this, so the distance is a little more than 56 miles. Since the net displacement has a large east component and a smaller north component, the direction lies between east and north. It is reasonable to describe this as towards the north east, or as slightly north of east, which justifies the approximate answer choice. Why Other Options Are Wrong: The option of approximately 40 miles towards the south west would require both net south and west components, which is opposite to the calculated 55 miles east and 12 miles north. The option of 30 miles towards the east underestimates the journey and ignores the significant northward displacement. The option of 25 miles towards the north is also too small and does not match the net east component. The alternative description of approximately 56 miles towards the east of north is close in magnitude but misstates the dominant direction, since the motion is mainly east with a slight north component, not mainly north. Common Pitfalls: Common mistakes include misinterpreting left and right turns, losing track of the current facing direction, and adding distances without considering direction signs. Some learners may incorrectly assume that the traveller returns close to the starting point and choose a small distance by guesswork. Drawing a simple diagram or coordinate table and breaking each leg into x and y components prevents these errors and makes the final Pythagorean calculation straightforward. Final Answer: The traveller ends up approximately 56 miles away from his starting point, located mainly to the east with some northward displacement, that is, approximately towards the north-east.

Question 10

Ravi starts walking from his house and goes 3 km towards the east to reach a bus stop. From the bus stop he boards a bus which goes straight in a direction towards his right for 4 km to reach his school. What is the straight line (crow flight) dista…

Accepted Answer

Introduction / Context: This question is a classic direction and distance problem in which a person moves along two perpendicular directions. The story talks about Ravi walking from his home to a bus stop and then travelling by bus to his school. We are asked to find the straight line distance between the home and the school, which is often referred to as crow flight distance in aptitude questions. Given Data / Assumptions: Ravi walks 3 km east from his house to reach the bus stop. At the bus stop he is facing east along his walking direction. The bus then moves straight towards his right for 4 km to reach the school. A right turn from facing east takes him towards the south. We assume the earth surface is locally flat and use standard north south east west axes. Concept / Approach: We can think of Ravi's movements as forming the two perpendicular legs of a right angled triangle. Walking east from home to the bus stop provides one horizontal leg, and the bus moving southwards gives a vertical leg. The crow flight distance between his home and school is the hypotenuse of this right angled triangle. The Pythagorean theorem is used to compute the length of this hypotenuse from the two perpendicular sides of 3 km and 4 km. Step-by-Step Solution: Step 1: Place Ravi's house at the origin (0, 0) on a coordinate plane with east as positive x and north as positive y.Step 2: After walking 3 km east, the bus stop is at (3, 0).Step 3: At the bus stop Ravi is facing east. A right turn from east means facing south.Step 4: The bus now travels 4 km south, so the school is at (3, −4).Step 5: The displacement from the house (0, 0) to the school (3, −4) is a right angled triangle with legs of 3 km east and 4 km south.Step 6: By the Pythagorean theorem, the distance d between home and school is d = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 km. Verification / Alternative check: We can confirm the result by recognising that 3, 4, and 5 form a very common Pythagorean triple. Whenever the horizontal and vertical legs are 3 units and 4 units, the hypotenuse is 5 units. Because the movements are purely east and south with no diagonal segments, the crow flight distance must be the hypotenuse, and 5 km is the only value that satisfies this relationship. This confirms that the school is 5 km away from the house in a straight line. Why Other Options Are Wrong: The option 1 km is far too small and does not fit any reasonable combination of 3 km and 4 km perpendicular legs. The option 7 km is larger than the sum of the legs and cannot be the hypotenuse of a right angled triangle of 3 km and 4 km. The option 12 km is simply the sum of 3 and 9 or other miscalculations and is not supported by the geometry. The value 4 km corresponds to only one of the legs and therefore is not the crow flight distance between two endpoints of the path. Common Pitfalls: A frequent mistake is to add the two distances, 3 km and 4 km, and assume that 7 km is the answer, ignoring the fact that the two legs are perpendicular. Another common error is misinterpreting right and left and drawing a wrong orientation, which changes the coordinates entirely. Drawing a simple right angled triangle and labelling the legs makes it easier to see that the hypotenuse must be computed using the square root of the sum of squares of the two legs. Final Answer: The straight line or crow flight distance between Ravi's house and his school is 5 km.

Question 11

Sumanth walks 200 feet straight from his house, which faces north, so he moves towards the north. Then he walks 100 feet in the reverse direction towards the south. After this he takes a left turn and walks 300 yards in that new direction. In which …

Accepted Answer

Introduction / Context: This question is about relative direction after a series of movements. Sumanth starts from his house, which is facing north, and walks forward, then backwards, and finally turns left and walks again. We need only the final direction of his position relative to the starting point, not the exact distance. Such questions are common in direction sense tests and require careful attention to current facing direction before interpreting left or right turns. Given Data / Assumptions: Sumanth's house faces north and he initially walks 200 feet straight towards the north. He then walks 100 feet in the reverse direction, which is towards the south. After that, he takes a left turn from his then facing direction. He walks 300 yards in this new direction, which is effectively a long move but only direction matters. We assume standard mapping of directions: north, south, east, and west with perpendicular relationships. Concept / Approach: We must track both his current position and the direction he is facing at each stage. Moving forward and then backward along the same straight line will partially cancel, leaving a smaller net displacement along the north south axis. The crucial step is to interpret the left turn correctly from the direction he is facing just before turning. The long final movement defines the horizontal component that will decide whether he is to the east or west of his starting point. Step-by-Step Solution: Step 1: Assume Sumanth starts from point O, which is his house.Step 2: His house faces north, so walking 200 feet straight means moving 200 feet north to point A. He is now 200 feet north of O and facing north.Step 3: He then walks 100 feet in the reverse direction, which is towards the south, returning part way towards O. After this, he is 200 − 100 = 100 feet north of O and facing south.Step 4: Now he takes a left turn from facing south. When facing south, left corresponds to east.Step 5: He walks 300 yards in the eastward direction. Since this final move is entirely towards the east, his final position is significantly east of O and still 100 feet north of O.Step 6: Therefore, relative to his original position at O, Sumanth is to the north east. Verification / Alternative check: We can visualise the path on a simple grid. Starting at O, he first goes up (north), then partially back down (south), ending slightly above the original point. The final long leg is horizontal to the right (east). Combining a small north displacement and a large east displacement clearly places him in the north east quadrant with respect to O. The exact distances, including the conversion of yards to feet, are not needed to determine direction, only their signs and relative orientation matter. Why Other Options Are Wrong: If he were in the south east, he would have to end up south of his starting point, which is impossible because his net north south displacement leaves him north of O. Similarly, south west and north west would require final westward displacement or net southward displacement at some stage, which does not happen here. Pure east is not correct because he is also north of O by 100 feet. Only north east captures the correct combination of being north and east of the starting point. Common Pitfalls: A typical mistake is to treat left and right turns as absolute east or west directions rather than relative to the current facing direction. Another error is to ignore the reverse movement and assume that travelling 200 feet north dominates completely, which would misplace his final position. Drawing a quick sketch with arrows for each move and labelling intermediate orientations will greatly reduce errors in these kinds of problems. Final Answer: After all the movements, Sumanth is towards the North-East of his original position at his house.

Question 12

Reena walks from point A to point B, 10 feet towards the east. Then she turns to her right and walks 3 feet. Again she turns to her right and walks 14 feet. At this stage, how far is she from her original point A?

Accepted Answer

Introduction / Context: This direction sense question involves Reena walking along a path that includes two right angle turns. The movements form a right angled shape on the ground. We are asked to determine the straight line distance between her final position and the starting point A. The underlying concept is basic right angled triangle geometry with short integer distances. Given Data / Assumptions: Reena starts from point A. She walks 10 feet east to reach point B. From there, she turns right, faces south, and walks 3 feet. Again she turns right from facing south, so she faces west and walks 14 feet. We need the straight line distance from her final position back to A. Concept / Approach: We will model Reena's movements using coordinates. Treating east as positive x and north as positive y, each step can be described as a change in x and y. After summing these changes, we obtain her final coordinates. The distance between the starting point and final point is then found using the Pythagorean theorem, because the path forms a right angled triangle whose legs are the horizontal and vertical displacements. Step-by-Step Solution: Step 1: Place point A at (0, 0).Step 2: After walking 10 feet east, Reena is at (10, 0) and facing east.Step 3: She turns right, which from east means facing south, and walks 3 feet to reach (10, −3).Step 4: She turns right again, which from south means facing west, and walks 14 feet to reach (−4, −3).Step 5: Her final position is at (−4, −3) relative to A at (0, 0).Step 6: The horizontal displacement is 4 feet west, and the vertical displacement is 3 feet south.Step 7: The straight line distance d between A and her final position is d = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 feet. Verification / Alternative check: We can verify the calculations by noting that the 3, 4, 5 triangle is a well known Pythagorean triple. Any right angled triangle with legs 3 and 4 has a hypotenuse of 5. Since Reena ends up 4 feet west and 3 feet south of the starting point, the triangle formed by her final position, the foot of a perpendicular on the starting vertical line, and point A is such a 3, 4, 5 triangle. Therefore, the direct distance from A to her final position must be exactly 5 feet. Why Other Options Are Wrong: The option 4 feet corresponds only to the horizontal separation and ignores the vertical displacement. The value 24 feet is the sum of some of the segments and does not measure the crow flight distance. Similarly, 27 feet is the sum of all three legs of the path and represents the total walking distance, not the straight line distance from the start. The 14 feet option corresponds to one of the walking segments but has nothing to do with the final displacement from A. Common Pitfalls: Some students confuse total path length with straight line distance and therefore add the legs 10, 3, and 14. Others misinterpret the turns and draw the last segment incorrectly to the east instead of west. Clearly marking the directions after each turn and plotting the path as a simple figure on grid paper are effective strategies to avoid these mistakes. Final Answer: The straight line distance between Reena's final position and the starting point A is 5 feet.

Question 13

A horse is initially facing north. It turns 90 degrees in the clockwise direction, then turns 180 degrees in the anti clockwise direction, and then turns another 90 degrees in the same anti clockwise direction. After performing all these turns, whic…

Accepted Answer

Introduction / Context: This problem involves sequential rotations and asks for the final facing direction. The horse starts facing north and then rotates through several angles in clockwise and anti clockwise directions. These types of questions test the ability to track orientation changes and understand that clockwise and anti clockwise rotations have opposite effects on final direction. Given Data / Assumptions: The horse begins facing north. It turns 90 degrees clockwise. Then it turns 180 degrees anti clockwise. Then it turns another 90 degrees in the same anti clockwise direction. We treat rotations in a full circle of 360 degrees with directions north, east, south, and west spaced 90 degrees apart. Concept / Approach: Instead of trying to visualise the horse turning physically, we can use angle measures on a circle. We choose a convention where north corresponds to 0 degrees, east to 90 degrees, south to 180 degrees, and west to 270 degrees. Clockwise rotation is treated as adding positive angles and anti clockwise as subtracting, or vice versa, as long as we remain consistent. The net effect of all rotations determines the final direction. Step-by-Step Solution: Step 1: Start with the horse facing north. Represent this as 0 degrees.Step 2: A 90 degree clockwise turn from north brings the horse to face east, which corresponds to 90 degrees.Step 3: Now a 180 degree anti clockwise turn from east subtracts 180 degrees, taking the horse from 90 degrees to −90 degrees, which is equivalent to 270 degrees and corresponds to west.Step 4: The horse then turns another 90 degrees anti clockwise. Subtracting 90 degrees from 270 degrees gives 180 degrees.Step 5: An orientation of 180 degrees corresponds to facing south.Step 6: Therefore, after all the turns, the horse is facing south. Verification / Alternative check: We can also track the directions without angles. From north, 90 degrees clockwise leads to east. From east, a 180 degree anti clockwise rotation takes us back through north to west. Finally, another 90 degree anti clockwise turn from west leads to south. Following the directions step by step confirms that the final facing direction is south, matching the angle based reasoning. Why Other Options Are Wrong: East would be correct if the final anti clockwise turn were not applied, because that was the direction after the first rotation. South west and south east are diagonal directions that require intermediate 45 degree rotations not specified here. North west would require ending 90 degrees away from north in the opposite direction, which does not match the combined rotations described. Only south fits the full sequence of 90 clockwise, 180 anti clockwise, and 90 anti clockwise rotations. Common Pitfalls: Students sometimes forget that clockwise and anti clockwise rotations have opposite signs and mistakenly add all angle values together without considering direction. Others stop tracking after the second rotation and ignore the last 90 degree turn. Using a rough sketch of a compass and marking each rotation one by one is a reliable way to avoid errors in such questions. Final Answer: After all the specified turns, the horse is facing towards the South.

Question 14

Early in the morning after sunrise, Karthik is standing in front of his house in such a way that his shadow falls exactly behind him. He then starts walking straight ahead for 5 metres, turns to his left and walks 3 metres, and again turns to his le…

Accepted Answer

Introduction / Context: This question combines knowledge about the position of the sun with direction sense and left right turns. Karthik stands so that his shadow is directly behind him in the morning, and then he walks and turns. We must use the information about the sun's position after sunrise to infer his initial facing direction, and then track his path to determine his final direction with respect to the starting point. Given Data / Assumptions: It is early morning just after sunrise, so the sun is in the east. Karthik stands so that his shadow falls directly behind him. He walks straight ahead for 5 metres from this position. Then he turns left and walks 3 metres. Again he turns left and walks 2 metres. We assume the directions follow the usual convention in which the sun rises in the east and shadows fall opposite to the sun. Concept / Approach: The first step is to find Karthik's initial facing direction. In the morning the sun is in the east, so a person whose shadow falls behind him must be facing away from the sun, that is, towards the west. Once we know he is facing west, we can interpret straight, left, and left again in terms of west, south, and east movements. Finally, we compare his ending position to the starting point and identify the overall direction such as south west or south east. Step-by-Step Solution: Step 1: Since it is after sunrise, the sun is in the east. Shadows fall away from the sun.Step 2: Karthik's shadow is directly behind him, which means he must be facing away from the east, that is, towards the west.Step 3: Take his starting point as the origin (0, 0). Facing west, he walks straight 5 metres to reach (−5, 0).Step 4: From facing west, a left turn means he now faces south. Walking 3 metres south leads to (−5, −3).Step 5: From facing south, another left turn makes him face east. Walking 2 metres east takes him to (−3, −3).Step 6: His final position is 3 metres west and 3 metres south of his starting point.Step 7: Therefore, with respect to the starting point, he is in the south west direction. Verification / Alternative check: We can quickly verify the initial facing direction by visualising. In the morning, the sun is in front if a person faces east and shadows fall behind towards the west. For the shadow to be behind while the sun is east, Karthik must face west. Once this is clear, the left turns can be tracked using a simple compass sketch: from west, left leads to south, and from south, left leads to east. The final coordinate calculation confirms that his displacement has both a south and west component, which identifies the south west direction uniquely. Why Other Options Are Wrong: If he were to the west of the starting point but not south, only pure west would be correct, but here he is also 3 metres south. North east and south east would have him east of the start, which does not match the negative x coordinate. Pure east is clearly incorrect because his main movement began towards the west. South east would place him in the opposite horizontal direction. Only south west fits both the horizontal and vertical displacement signs. Common Pitfalls: Learners often misinterpret the effect of sunlight on shadows and may wrongly assume that facing east gives a shadow behind in the morning. Another frequent error is mixing up left and right when the person is facing west or south, which reverses directions. Drawing the four cardinal directions and following the turns step by step helps avoid confusion and ensures that both the initial orientation and turns are handled correctly. Final Answer: After all his movements, Karthik is located in the South-West direction from his original starting position in front of his house.

Question 15

In a certain symbolic notation for directions, A x B means A is to the south of B, A + B means A is to the north of B, A % B means A is to the east of B and A - B means A is to the west of B. Using this notation, in the expression P % Q + R - S, in …

Accepted Answer

Introduction / Context: This question tests the ability to interpret symbolic relations that encode positions in terms of directions. Instead of directly stating that one point is north, south, east, or west of another, symbols like x, +, %, and - are used. The target is to parse a compound expression involving P, Q, R, and S and then determine the relative direction of S with respect to Q. This type of coding is common in reasoning tests. Given Data / Assumptions: A x B means A is to the south of B. A + B means A is to the north of B. A % B means A is to the east of B. A - B means A is to the west of B. The given expression is P % Q + R - S. We interpret each pair in the expression separately, maintaining relative positions consistently in a coordinate plane. Concept / Approach: The expression P % Q + R - S can be broken into three relationships: P % Q, Q + R, and R - S. From these, we can deduce the positions of P, R, and S relative to Q, treating Q as a reference. Using coordinate style reasoning, we can assign Q any convenient position, for example the origin, and then place the other points accordingly. The final coordinate of S relative to Q will reveal the direction of S with respect to Q. Step-by-Step Solution: Step 1: Interpret P % Q. Since A % B means A is to the east of B, P % Q means P is east of Q.Step 2: Interpret Q + R. Since A + B means A is to the north of B, Q + R means Q is north of R, so R is south of Q.Step 3: Interpret R - S. Since A - B means A is to the west of B, R - S means R is west of S, so S is east of R.Step 4: Place Q at the coordinate (0, 0) on a grid, with east as positive x and north as positive y.Step 5: Since R is south of Q, place R at (0, −1). The exact distance is not important, only relative direction matters.Step 6: Since S is east of R, place S at (1, −1).Step 7: The displacement from Q at (0, 0) to S at (1, −1) involves moving one step east and one step south, which is the south east direction. Verification / Alternative check: We can also verify without coordinates by reasoning verbally. If R is south of Q and S is east of R, then S is south and east from Q when both relationships are combined. Any consistent picture of Q at the centre, R directly below Q, and S further to the right of R will show S lying diagonally down and to the right of Q. This is the south east direction. Because the expression does not constrain any other orientation, the south east inference is robust. Why Other Options Are Wrong: The north west direction would require S to be both north and west of Q, which contradicts the established facts that R is south of Q and S is east of R. Pure east or pure west would require no vertical displacement relative to Q, whereas here S is explicitly south of Q. South west would require the point to be west of Q, which is not consistent with S being east of R and R being directly south of Q. Therefore, only south east matches the combined relational data. Common Pitfalls: Many learners misread the compound expression and try to apply all operations from left to right without breaking them into pairwise relations. Another common error is to place R north of Q instead of south when interpreting Q + R. Using a simple coordinate diagram and writing down each relationship helps prevent such mistakes. It is also useful to remember that the first symbol in A x B describes the position of A relative to B and not the other way around. Final Answer: In the configuration described by P % Q + R - S, point S lies in the South-East direction with respect to point Q.

Question 16

Sundar runs 20 metres towards the east and then turns to his right and runs 10 metres. Next, he turns to the right again and runs 9 metres. Again he turns to the right and runs 5 metres. After this, he turns to the left and runs 12 metres and finall…

Accepted Answer

Introduction / Context: The focus of this question is not the final position but the final facing direction of Sundar after a sequence of runs and turns. He starts by moving east and then repeatedly turns right or left and runs certain distances. Such problems strengthen the ability to track orientation step by step, which is important in the direction sense portion of verbal reasoning tests. Given Data / Assumptions: Sundar first runs 20 metres towards the east. He then turns right and runs 10 metres. He turns right again and runs 9 metres. He turns right once more and runs 5 metres. Next, he turns left and runs 12 metres. Finally, he turns right and runs 6 metres. We use the usual convention: right turn is clockwise relative to the current facing, left turn is anticlockwise. Concept / Approach: We are only asked about the final facing direction, so exact coordinates are not required. The strategy is to track Sundar's orientation after each turn. Starting from east, we know that a right turn takes him to south, another right to west, and another right to north. Then a left from north returns him to west, and a final right from west takes him back to north. Keeping a small compass sketch handy is very helpful for such stepwise orientation tracking. Step-by-Step Solution: Step 1: Sundar begins by running east, so his initial facing direction is east.Step 2: He turns right from east, which makes him face south, and he runs 10 metres. Distance is not important for orientation.Step 3: He turns right again from south, which makes him face west, and he runs 9 metres.Step 4: He turns right once more from west, which makes him face north, and he runs 5 metres.Step 5: He then turns left from north, which makes him face west, and runs 12 metres.Step 6: Finally, he turns right from west, which makes him face north, and runs 6 metres.Step 7: At the end of all movements, Sundar is therefore facing north. Verification / Alternative check: We can summarise the sequence of directions as follows: start east, then south, then west, then north, then west, then north. At each turn we rotate by 90 degrees either clockwise or anticlockwise depending on right or left. Tracing this on a small compass diagram confirms that the final orientation is north. Because distances do not alter orientation, any confusion about the lengths of the segments will not affect this conclusion. Why Other Options Are Wrong: East would be correct only if there were an even number of right angle turns bringing Sundar back to his original orientation, which is not the case here. West and south appear as intermediate facing directions but are not the last one after the full sequence. South east is a diagonal direction and would require non right angle turns or partial rotations, which do not occur anywhere in the problem. Only north matches the final direction reached after processing all given turns. Common Pitfalls: One common mistake is to attempt to track both distance and direction simultaneously, which can lead to overload and errors. Focus should remain on the orientation only. Another pitfall is mixing up left and right when the person is facing south or west, because the mental picture has rotated. Using a fixed compass drawing and marking each step is an effective way to avoid these issues. Final Answer: After completing all the runs and turns, Sundar is finally facing towards the North.

Question 17

Two persons P and Q are initially separated by a distance of 20 metres along a west east line, with P in the west and Q in the east. Now P and Q start walking, P towards the north and Q towards the south, and each walks 5 metres. Then both take a ri…

Accepted Answer

Introduction / Context: This direction sense question requires tracking the movements of two people, P and Q, who start at different positions and walk in different directions. After a series of moves and turns, we need to find the distance between their final positions. Questions like this encourage careful use of a coordinate system or diagram to avoid mixing up left and right or miscounting distances. Given Data / Assumptions: Initially, P and Q are 20 metres apart on a west east line, P in the west and Q in the east. P walks 5 metres north, Q walks 5 metres south. Then both take a right turn and walk 10 metres each. After that, both take a left turn and walk 5 metres each. Standard convention is used: right turn is clockwise relative to the current facing direction, left is anticlockwise. The task is to calculate the straight line distance between P and Q at the end. Concept / Approach: We use a simple coordinate system with east as positive x and north as positive y. We set P at (0, 0) and Q at (20, 0) initially. We track each movement of P and Q step by step, updating their coordinates based on direction and distance. The final distance between them is obtained using the distance formula between two points. If this distance does not match any of the explicit numerical options, the correct answer is the option representing none of these. Step-by-Step Solution: Step 1: Place P at (0, 0) and Q at (20, 0).Step 2: P walks 5 metres north to (0, 5). Q walks 5 metres south to (20, −5).Step 3: At this stage, P faces north and Q faces south.Step 4: Both take a right turn. P's right from north is east, so P walks 10 metres east to (10, 5). Q's right from south is west, so Q walks 10 metres west to (10, −5).Step 5: Now both face their new directions (P facing east, Q facing west) and then take a left turn. P's left from east is north, so P walks 5 metres north to (10, 10). Q's left from west is south, so Q walks 5 metres south to (10, −10).Step 6: The final coordinates are P at (10, 10) and Q at (10, −10).Step 7: The distance between these points is |10 − (−10)| along the y axis, which equals 20 metres. Verification / Alternative check: We can observe that both P and Q end up directly above and below the same x coordinate, x = 10. Their vertical separation is twice the distance from the horizontal axis, since P is 10 units above and Q is 10 units below, making the total vertical separation 20 metres. There is no horizontal separation at the end, so the straight line distance equals this vertical separation. Because 20 metres does not appear among the numeric choices a, b, or c, the answer must be the option that states none of these. Why Other Options Are Wrong: The option 15 metres would require each to be 7.5 metres above and below the midline, which does not match the movements. The option 25 metres is larger than any plausible separation given the step sizes. The option 30 metres is even more extreme and has no basis in the described paths. The value 20 metres is correct but appears only indirectly as our calculation, so among the listed options only the choice labelled none of these matches the true situation. Common Pitfalls: A common error is to treat right and left turns as absolute directions rather than relative to north and south, which can place P and Q in completely wrong quadrants. Another mistake is to attempt to mentally add distances without using coordinates or a diagram, leading to miscalculations of their final separation. Drawing a coordinate grid or at least a rough sketch and marking each leg of the journey is the safest way to avoid such errors. Final Answer: The final distance between P and Q is 20 metres, which does not appear among the explicit numeric options, so the correct choice is None of these.

Question 18

A man is facing towards the east. He then turns 270 degrees in the clockwise direction and after that takes a right turn. Finally, he turns 90 degrees in the anti clockwise direction. After performing all these turns, which direction is he facing no…

Accepted Answer

Introduction / Context: This problem deals purely with rotations and asks for the final facing direction of a man after several turns. He starts by facing east, then turns through a large clockwise angle, takes a right turn, and finally turns anti clockwise. Such questions test clarity about clockwise versus anti clockwise direction and how right and left turns relate to current orientation. Given Data / Assumptions: The man initially faces east. He turns 270 degrees clockwise. Then he takes a right turn. Finally, he turns 90 degrees anti clockwise. We consider the basic compass directions: north, east, south, and west spaced at 90 degree intervals. Concept / Approach: A simple and reliable method is to track the direction after each turn rather than trying to combine all angles at once. A 270 degree clockwise turn is equivalent to a 90 degree anti clockwise turn, because both leave the person in the same direction relative to the start. After this, a right turn means another 90 degree clockwise rotation from the current facing direction. Finally, we subtract 90 degrees for the anti clockwise turn and see where we end up on the compass. Step-by-Step Solution: Step 1: The man begins facing east.Step 2: A 270 degree clockwise turn from east is the same as a 90 degree anti clockwise turn. Starting from east, a 90 degree anti clockwise turn leads to north.Step 3: Now he is facing north. A right turn from north is a 90 degree clockwise turn, which leads to east.Step 4: After this right turn, he is facing east again.Step 5: Finally, he turns 90 degrees anti clockwise from east, which leads back to north.Step 6: Therefore, after all rotations and turns, he is facing north. Verification / Alternative check: We can represent directions as angles on a circle: east as 90 degrees, south as 180 degrees, west as 270 degrees, and north as 0 or 360 degrees. Starting from east at 90 degrees, adding 270 degrees clockwise gives 360 degrees, which is equivalent to north. A right turn from north adds 90 degrees and returns to east at 90 degrees. Subtracting 90 degrees for the anti clockwise final turn brings us back to 0 degrees, or north. This angle based check agrees entirely with the stepwise direction tracking. Why Other Options Are Wrong: West would be correct if there were an extra 90 degree clockwise turn after the last step, but that is not described. South would require the final total rotation to land at 180 degrees, which does not happen. Remaining in east would only occur if the final anti clockwise turn were not made. South east is a diagonal direction and is not reachable through these exact quarter turns. Therefore, only north matches the combined effect of all the given rotations. Common Pitfalls: Many candidates misinterpret the 270 degree clockwise turn as leading directly to south because they mistakenly subtract 90 degrees instead of adding 270 to the initial angle. Others lose track of the orientation after the right turn and apply the last 90 degree anti clockwise rotation from the wrong starting direction. Drawing a compass and marking each step carefully avoids such confusion. Final Answer: After completing all the described turns, the man is facing towards the North.

Question 19

A compass is incorrectly aligned. For the true direction of west, the compass needle is showing south west. Assuming the same misalignment for all directions, what direction will the compass show when the person is actually facing true north?

Accepted Answer

Introduction / Context: This question is about an incorrectly aligned compass that shows wrong directions. We are told how the compass reading differs from the true direction for west and are asked what it would show for true north. The problem deals with the concept of a fixed angular error in the compass reading and requires applying the same error to another cardinal direction. Given Data / Assumptions: For the true direction west, the compass shows south west. South west is 45 degrees away from west on a standard compass. The misalignment is assumed to be constant for all directions. We must determine what the compass will indicate when the user is actually facing true north. We use the standard positions: north at 0 degrees, east at 90 degrees, south at 180 degrees, west at 270 degrees, south west at 225 degrees, and north west at 315 degrees. Concept / Approach: The key is to understand that the compass reading is rotated by a fixed angle relative to the true direction. Since true west (270 degrees) is shown as south west (225 degrees), the reading is 45 degrees less than the true direction. In other words, the compass subtracts 45 degrees from every true direction. To find what it shows for true north, we subtract the same 45 degrees from the north direction and then map the result back to a compass point, taking care to work modulo 360 degrees. Step-by-Step Solution: Step 1: Represent west as 270 degrees and south west as 225 degrees on the compass.Step 2: The difference between the compass reading and the true direction is 225 − 270 = −45 degrees, meaning the reading is rotated 45 degrees anticlockwise from the true direction.Step 3: Assume this error is the same for every direction. For a true direction of north, which is 0 degrees, the compass reading will be 0 − 45 degrees.Step 4: Subtracting 45 degrees from 0 degrees gives −45 degrees, which is equivalent to 315 degrees when we add 360 degrees to stay within a full circle.Step 5: An angle of 315 degrees corresponds to the north west direction on a compass.Step 6: Therefore, when facing true north, the misaligned compass will show north west. Verification / Alternative check: We can quickly recheck the logic by applying the same reasoning to another direction. For example, true south at 180 degrees would be shown as 180 − 45 = 135 degrees, which is south east. This is consistent with the idea that every reading is shifted 45 degrees anticlockwise. Returning to north, 0 degrees minus 45 degrees must wrap around the circle, landing at 315 degrees. This corresponds to north west and confirms that our initial calculation is correct. Why Other Options Are Wrong: East corresponds to 90 degrees and would be the reading if the compass added 90 degrees rather than subtracting 45 degrees, which contradicts the given misalignment. North east at 45 degrees would require a shift of only 45 degrees from north, but in the wrong direction for the described error. South east and south west lie in the opposite half of the compass and do not follow from applying the same anticlockwise shift that moves west to south west. Only north west matches the computed 315 degree reading. Common Pitfalls: Some learners mistakenly think that if west is shown as south west, then north must be shown as north east by moving in the same direction on the compass card, without considering angles. Another error is to add 45 degrees instead of subtracting it when moving from west to its erroneous reading. Being precise about angles and remembering to use a consistent sign for the error helps to avoid these mistakes. Final Answer: When the person is actually facing true north, the misaligned compass will show the direction as North-West.

Question 20

Kamal starts walking from his home facing the west direction. He walks 10 km towards the west, then takes a right turn and walks another 10 km. He again takes a right turn and walks 10 km to reach his school. How far, in kilometres, and in which dir…

Accepted Answer

Introduction / Context: This direction sense question describes Kamal walking a rectangular path. He starts facing west, walks straight, turns right, walks again, turns right once more, and reaches his school. The task is to find the straight line distance and direction from his home to the school. This is a typical problem where the path forms a rectangle and the net displacement is along one side of that rectangle. Given Data / Assumptions: Kamal starts from his home facing west. He walks 10 km towards the west. He takes a right turn and walks 10 km. He takes another right turn and walks 10 km to reach his school. He turns at right angles, and there is no diagonal movement. We use standard compass directions with perpendicular north south and east west axes. Concept / Approach: We model Kamal's motion on a coordinate plane. Moving west from home shifts him along the negative x axis. Turning right from west leads him to face north, and another right from north makes him face east. When he eventually reaches his school, the coordinates of the school relative to the home can be found by summing the horizontal and vertical displacements. The straight line distance is then simply the length of this net displacement and the direction is identified by the sign of the components. Step-by-Step Solution: Step 1: Let Kamal's home be at (0, 0).Step 2: Walking 10 km west takes him to (−10, 0). He is now facing west.Step 3: A right turn from west makes him face north. Walking 10 km north takes him to (−10, 10).Step 4: Another right turn from north makes him face east. Walking 10 km east brings him to (0, 10).Step 5: The coordinates of his school are (0, 10) relative to his home at (0, 0).Step 6: The net displacement is 10 km north and 0 km east or west, so the straight line distance is 10 km in the north direction. Verification / Alternative check: The path described forms three sides of a rectangle with sides 10 km by 10 km. Kamal starts at one corner, walks along the bottom side to the left, then up the left side, and then along the top side back to the right. This leaves him directly above his starting point, at the opposite corner vertically. Hence the distance from home to school equals the height of the rectangle, which is 10 km, and the direction is straight north. This geometric view agrees with the coordinate reasoning. Why Other Options Are Wrong: The option 10 km south would place the school on the opposite side of the home relative to the actual path. The options 20 km north east and 20 km south west grossly overestimate the distance and introduce a diagonal that does not exist in the described path. The option of 0 km would mean he returns exactly to his house, which he does not, because he has only walked three sides of the rectangle, not all four. Only 10 km north matches the net displacement. Common Pitfalls: A frequent error is to assume that walking 10 km west followed by two right turns and two more 10 km legs must bring him back home, forgetting that a full loop requires four sides. Another mistake is to mix up right and left turns when facing west or north, which changes the shape of the path. Sketching a rectangle and labelling each leg in order helps make the relative positions of home and school obvious. Final Answer: Kamal's school is located 10 km to the North of his home.

Direction Sense Test Questions