Question 1

Rahul moves 5 km towards the South from his initial position and then takes a left turn to move 5 km. Again, he takes another left turn and moves 10 km, and finally he moves 5 km towards the West. In which direction is he now located from his initia…

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Introduction / Context: This direction sense question describes Rahul walking along several straight segments involving two left turns and one final absolute movement towards the West. We are asked to determine only the final direction of Rahul with respect to his starting point, not the exact distance. By breaking his route into horizontal and vertical displacements, we can identify whether he ends up North, South, East, West or in one of the diagonal quadrants relative to the initial position. Given Data / Assumptions: Rahul starts from an initial position. He moves 5 km towards the South. He then takes a left turn and moves 5 km. Again, he takes a left turn and moves 10 km. Finally, he moves 5 km towards the West (absolute direction). All turns are 90 degree turns. We assume that from facing South, a left turn leads to East, and from facing East, a left turn leads to North. Concept / Approach: We model Rahul's path on a coordinate grid, converting each movement into x (East–West) and y (North–South) components. By adding up all the components, we get his final coordinates relative to the origin. The sign and magnitude of the final coordinates tell us the direction in which he lies from the starting point. In this case, we will find that the net horizontal displacement is zero, while there is a net positive vertical displacement, indicating a final direction of North. Step-by-Step Solution: Step 1: Place Rahul's initial position at (0, 0). Step 2: Moving 5 km South takes him to (0, -5); he is facing South. Step 3: From facing South, a left turn makes him face East. Moving 5 km East takes him to (5, -5). Step 4: From facing East, another left turn makes him face North. Moving 10 km North takes him to (5, 5). Step 5: Finally, he moves 5 km towards the West, which is an absolute direction. This changes only the x-coordinate, moving him from (5, 5) to (0, 5). Step 6: The final coordinates are (0, 5). Compared with the starting point (0, 0), Rahul is 5 km North and 0 km East–West. Hence he is directly North of his starting point. Verification / Alternative check: We can verify by separately summing the vertical and horizontal components. For vertical movement, he goes 5 km South and then 10 km North, giving a net displacement of 10 − 5 = 5 km North. For horizontal movement, he goes 5 km East and 5 km West, which cancel out to zero. With a positive net North component and zero East–West component, his final direction must be exactly North of the starting position. A rough sketch of the path confirms that he ends up above the starting point in a straight vertical line. Why Other Options Are Wrong: West would require a net horizontal displacement to the left of the origin, but we found that East and West movements cancel entirely. East is similarly ruled out because there is no net rightward movement. South is incorrect because Rahul ends up North of the starting point, not below it. South-West would require both Southward and Westward net displacement; neither condition holds once cancellations are considered. Common Pitfalls: Many candidates treat the final Westward movement as if it dominates the path, forgetting that earlier Eastward movement cancels it. Others misinterpret left turns from South and East, sometimes swapping East and West or North and South. Keeping a simple coordinate tally or drawing the path step by step is the best way to avoid these errors and quickly see the true final direction. Final Answer: Rahul is finally located directly to the North of his initial position.

Question 2

Deepak starts walking straight towards the East from a point and covers 75 metres. He then turns to his left and walks 25 metres straight, turns left again and walks 40 metres straight, and once more turns to his left and walks another 25 metres. Ho…

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Introduction / Context: This question describes Deepak walking along four straight segments with three left turns. We are asked to find the straight-line distance from his final position back to his starting point. Because the path contains several right-angle turns, the resultant displacement can be found using basic coordinate geometry and Pythagoras theorem after simplifying the net horizontal and vertical movements. Given Data / Assumptions: Deepak starts walking towards the East and covers 75 metres. He then turns left and walks 25 metres straight. Again, he turns left and walks 40 metres straight. Once more, he turns left and walks 25 metres. All turns are 90 degree left turns and all segments are straight. Standard direction convention is used: from East, left is North; from North, left is West; from West, left is South. Concept / Approach: We assign coordinates to each position by treating the starting point as the origin. East–West movements change the x-coordinate, and North–South movements change the y-coordinate. After tracking all four segments, we compute the straight-line distance between the starting and final coordinates using Pythagoras theorem: distance^2 = (Δx)^2 + (Δy)^2. Because some vertical movements cancel, the computation turns out to be straightforward. Step-by-Step Solution: Step 1: Place Deepak's starting point at (0, 0). Step 2: He walks 75 m East, reaching (75, 0). He is facing East. Step 3: From facing East, a left turn means facing North. Walking 25 m North takes him to (75, 25). Step 4: From facing North, a left turn means facing West. Walking 40 m West brings him to (35, 25). Step 5: From facing West, another left turn faces him South. Walking 25 m South takes him to (35, 0). Step 6: His final coordinates are (35, 0), while his starting point is (0, 0). Therefore, the straight-line distance between the two points is the horizontal difference: |35 − 0| = 35 metres. Verification / Alternative check: Instead of computing coordinates, we can consider net horizontal and vertical displacement. Horizontally, Deepak walks 75 m East and 40 m West, so net Eastward displacement is 75 − 40 = 35 m. Vertically, he walks 25 m North and 25 m South, which cancel each other out, leaving zero net vertical displacement. Thus, his final position is directly East of the starting point by 35 m. There is no need for Pythagoras here because the displacement is purely horizontal, confirming that 35 m is the correct distance. Why Other Options Are Wrong: 50 m would arise if someone incorrectly subtracted or added the wrong distances or assumed a diagonal separation. 115 m and 140 m are simply the sums of some path segments and do not represent the straight-line distance from start to end. 25 m might be mistaken for the vertical leg alone, ignoring the larger Eastward net displacement. Since the net vertical displacement is zero, any answer that does not reflect a pure 35 m Eastward movement is incorrect. Common Pitfalls: Many students mistakenly add all distances to get the answer, confusing path length with displacement. Others might misinterpret left turns or neglect the fact that some movements cancel each other out. Carefully tracking each segment on a simple diagram, or writing down the cumulative x and y coordinates after each move, avoids such errors and helps you see that the final position is just 35 m East of the starting point. Final Answer: Deepak is now 35 m away from his starting point, directly to the East.

Question 3

Ajit starts from a fixed point and walks 10 m towards the North. He then turns to his right and walks another 10 m. After that, he successively turns to his left and walks 5 m, then turns left again and walks 10 m, and finally turns left once more a…

Accepted Answer

Introduction / Context: Ajit's motion in this problem involves several turns and different distances, forming a somewhat zig-zag path on the plane. Our goal is to find his straight-line distance from the starting point after all movements. This is another classic direction sense and displacement question where we track each segment on a coordinate grid and then apply basic geometry to compute the final separation between the starting and ending positions. Given Data / Assumptions: Ajit starts from a fixed point. He walks 10 m towards the North. He then turns right and walks 10 m. He successively turns left and walks 5 m, then left again and walks 10 m, and then left once more and walks another 10 m. All right and left turns are 90 degree turns. We use the standard convention for directions: from North, right is East; from East, left is North; from North, left is West; from West, left is South. Concept / Approach: It is convenient to represent Ajit's movement on a coordinate plane with the starting point as the origin. Each segment then corresponds to a change in x or y coordinates. By following the direction of each segment and updating the coordinates, we can determine the final point. The straight-line distance from the origin to this final point is then calculated using Pythagoras theorem if needed. In this specific problem, we will see that the final displacement is purely vertical, making the distance calculation straightforward. Step-by-Step Solution: Step 1: Place Ajit's starting point at (0, 0). Step 2: He walks 10 m North to reach (0, 10); he is facing North. Step 3: From facing North, a right turn makes him face East. Walking 10 m East takes him to (10, 10). Step 4: From facing East, a left turn faces him North. Walking 5 m North moves him to (10, 15). Step 5: From facing North, another left turn faces him West. Walking 10 m West takes him to (0, 15). Step 6: From facing West, another left turn faces him South. Walking 10 m South moves him to (0, 5). Step 7: His final coordinates are (0, 5). The starting point is (0, 0). The straight-line distance between these points is |5 − 0| = 5 m. Verification / Alternative check: Compute net horizontal and vertical movement. Horizontally, Ajit moves 10 m East and later 10 m West, which cancel each other, so his net East–West displacement is 0. Vertically, he moves 10 m North, then 5 m North, and finally 10 m South. Net vertical displacement = 10 + 5 − 10 = 5 m North. Therefore, he ends up 5 m directly North of the starting point, confirming that the distance from the start is 5 m and that the displacement is purely vertical. Why Other Options Are Wrong: 15 m and 10 m are larger distances that might be obtained by incorrectly adding path segments without considering direction or cancellations. 3 m is not supported by any combination of right-angle geometry in this problem. 0 m would imply that Ajit returned exactly to his starting point, which is not the case here; his final coordinates are clearly different from the origin. Because only the 5 m displacement matches both the coordinate tracking and the net component calculation, the other options are incorrect. Common Pitfalls: Some learners confuse the sequence of left turns after the first right turn, accidentally swapping North and South or East and West at some step. Others might attempt to calculate distance by adding all the given segments, which gives the path length but not the displacement from the starting point. Maintaining a clear step-by-step record of coordinates or drawing the path on a simple grid is an effective strategy to avoid these mistakes. Final Answer: Ajit is now 5 m away from his starting point.

Question 4

An office worker walks 4 km towards the East from his home to reach a taxi-stand. He then takes a taxi which goes 10 km towards the South, turns right and goes a further 15 km, where he gets down and boards a bus. The bus travels 2 km towards the No…

Accepted Answer

Introduction / Context: This is a multi-stage direction sense problem where an office worker first walks, then travels by taxi, and finally by bus. Each leg of the journey involves different directions and distances. Our task is to determine the final position of the office with respect to his home. Even though the description is lengthy, the underlying method is the same as in simpler problems: track horizontal and vertical components of each segment and compute the net displacement. Given Data / Assumptions: The worker walks 4 km East from his home to reach a taxi-stand. The taxi goes 10 km South, then turns right and goes 15 km further. At that point, the worker gets down and boards a bus. The bus travels 2 km North, then 3 km West, and finally turns right and travels 8 km. All turns described as “right” are 90 degree turns, and all segments are straight. We use standard orientation: from South, right is West; from West, right is North. We must find the office's location relative to the worker's home. Concept / Approach: We treat the entire journey as movement on a coordinate plane, taking the home as the origin. Each leg of the walk, taxi ride and bus ride shifts the worker's position by some amount in the East–West or North–South direction. By summing these shifts step by step, we find the final coordinates of the office relative to the home. Once we know the final x and y coordinates, we can answer the question about how far East or West and North or South the office lies from the home. Step-by-Step Solution: Step 1: Let the worker's home be at (0, 0). Step 2: Walking 4 km East to the taxi-stand takes him to (4, 0). Step 3: The taxi first goes 10 km South, moving him to (4, -10). Step 4: From facing South, a right turn means facing West. The taxi then travels 15 km West, bringing him to (4 − 15, -10) = (-11, -10). Step 5: He boards a bus at (-11, -10). The bus first travels 2 km North, taking him to (-11, -8). Step 6: Then the bus travels 3 km West, reaching (-14, -8). Step 7: At this point, the bus is facing West. A right turn from West means facing North. The bus then travels 8 km North, moving to (-14, 0). Step 8: The final coordinates of the office are (-14, 0) relative to the home at (0, 0). This means the office is 14 km to the West of the home and at the same North–South level. Verification / Alternative check: We can verify by summing horizontal and vertical components. Horizontally, the worker moves: 4 km East (home to taxi), 15 km West (by taxi), 3 km West (by bus). Net horizontal movement = 4 East − 15 West − 3 West = 4 − 18 = -14 km, i.e. 14 km West. Vertically, he moves 10 km South, 2 km North and 8 km North, for a net vertical displacement of -10 + 2 + 8 = 0 km. So there is no net North–South shift. The final position is therefore 14 km West of the starting point, matching the coordinate calculation. Why Other Options Are Wrong: 22 km West or 22 km East correspond to incorrect net horizontal sums and do not reflect the cancellation of some movements. 14 km East would require a net positive horizontal displacement, whereas we clearly have a net movement to the West (negative x-direction). 10 km South would only be true after the first taxi leg; subsequent movements cancel that vertical displacement, bringing him back to the same North–South level as his home. Therefore, all options except 14 km West are inconsistent with the step-by-step analysis. Common Pitfalls: Because the question mixes different modes of transport, some test-takers forget to track the direction changes coherently across segments. Another pitfall is to confuse the effect of “right” turns from different starting orientations, for example thinking that a right turn from West leads to South instead of North. Maintaining a consistent coordinate system and clearly noting each orientation before a turn are crucial strategies for avoiding these errors. Final Answer: The office is located 14 km West of the worker's home.

Question 5

Sunita starts from a fixed point and travels 6 km towards the north-east, then 9 km towards the west, then 6 km towards the south-west and finally 3 km towards the east. How far is she from her initial position?

Accepted Answer

Introduction / Context: In this direction sense question, Sunita walks in four different directions, including two diagonal directions. The task is to calculate how far she is from her initial starting point after completing the full path. This type of problem tests spatial visualization, vector addition and understanding of north-east and south-west movements on a coordinate plane. Given Data / Assumptions: - Sunita starts from an origin point, which we can treat as (0, 0) on a coordinate grid. - First she travels 6 km towards the north-east. - Then she travels 9 km towards the west. - Next she travels 6 km towards the south-west. - Finally she travels 3 km towards the east. - Directions follow the usual convention: east is positive x, north is positive y. Concept / Approach: To solve this, we break each movement into horizontal (east west) and vertical (north south) components. Movements purely west or east affect only the x coordinate. Movements purely north or south affect only the y coordinate. Movements towards north east or south west are along a 45 degree diagonal, so their x and y components have equal magnitude. By adding all horizontal components together and all vertical components together, we obtain the final coordinates. The straight line distance from the starting point is then the length of the resulting vector. In this particular case the vertical components cancel and the horizontal components simplify to an exact integer distance. Step-by-Step Solution: 1. Represent the north east movement of 6 km as equal components: 6 / sqrt(2) km east and 6 / sqrt(2) km north. 2. After this first move Sunita is at approximately (4.24 km east, 4.24 km north). 3. The second move is 9 km west, which reduces only the x coordinate: new x = 4.24 - 9 ≈ -4.76 km, y remains about 4.24 km. 4. The third move is 6 km towards the south west, again at 45 degrees, so the components are 6 / sqrt(2) km west and 6 / sqrt(2) km south. 5. Subtract these components: x ≈ -4.76 - 4.24 = -9 km, y ≈ 4.24 - 4.24 = 0 km. 6. The fourth move is 3 km east, so x = -9 + 3 = -6 km, y remains 0 km. 7. The final position is therefore 6 km to the west of the starting point on the same horizontal line. Verification / Alternative check: We can avoid decimals by reasoning symbolically. The first and third diagonal moves are equal in length and opposite in direction: north east versus south west. Their vertical components cancel exactly and their horizontal components also cancel. Therefore, these two diagonal legs together contribute net zero displacement. What remains is simply a 9 km west movement followed by a 3 km east movement. That simplifies to a net 6 km west displacement. A quick sketch on squared paper will show that Sunita ends up directly west of the start, on the same east west line, confirming the reasoning. Why Other Options Are Wrong: - 3 km is half of the correct horizontal displacement and would arise from incorrectly subtracting 9 - 6 instead of 9 - 3. - 9 km would be correct only if the final 3 km east movement were ignored. - 12 km assumes that all west movements are simply added without considering the final east movement. - 15 km is an overestimate that ignores both cancellation of diagonal legs and the final balancing movement. Common Pitfalls: A common mistake is to treat diagonal movements as if they were purely horizontal or purely vertical, which changes the total displacement. Another frequent error is to sum all distances walked instead of the net displacement, forgetting that the question asks for the straight line distance from the starting point, not total distance travelled. Some learners also forget that opposite legs of equal length in opposite diagonal directions cancel out when computing net displacement. Careful separation of x and y components avoids all these errors. Final Answer: Sunita is 6 km away from her initial position, directly to the west of the starting point.

Question 6

Ram walks 3 km towards the east, then turns left and walks 1 km, then turns left again and walks 2 km and finally turns left once more and walks 1 km. How far is he from his starting point?

Accepted Answer

Introduction / Context: This problem is a basic direction sense question involving right angles and short distances in a grid like path. Ram makes three left turns and walks different distances. We are asked for his straight line distance from the starting point after completing all legs of the journey. Such questions test the ability to track relative positions and use simple geometry without getting confused by the wording. Given Data / Assumptions: - Ram begins at a starting point that we treat as the origin. - He walks 3 km towards the east. - He then turns left, which from east means turning towards the north, and walks 1 km. - He then turns left again, which from north means turning towards the west, and walks 2 km. - Finally he turns left once more, which from west means turning towards the south, and walks 1 km. - Directions follow the usual compass convention on a flat plane. Concept / Approach: The most direct method is to track Ram's coordinates step by step. We consider east as the positive x direction and north as the positive y direction. Each movement changes either x or y because all turns are exactly 90 degrees. After all moves, we compare the final coordinates with the origin. The straight line distance from start is simply the absolute difference along the nonzero axis because, in this particular path, he ends on the same east west line as the start. Step-by-Step Solution: 1. Start at (0, 0). 2. Move 3 km east: new position is (3, 0). 3. Turn left to face north and walk 1 km: new position is (3, 1). 4. Turn left to face west and walk 2 km: new position is (1, 1). 5. Turn left again to face south and walk 1 km: new position is (1, 0). 6. From the origin (0, 0) to (1, 0) the difference is 1 km along the east west axis. Verification / Alternative check: Instead of coordinates, imagine the path as a rectangle. Ram first goes 3 km east and 1 km north. Then by going 2 km west and 1 km south he almost returns to his original east west line. At the end he is 1 km east of the starting line and back at the same north south level as the origin. A quick sketch of the path shows that his final position is exactly 1 km to the east of the starting point. This confirms the coordinate based calculation. Why Other Options Are Wrong: - 2 km would result from mistakenly subtracting 3 - 1 - 2 or misreading one of the legs. - 3 km corresponds to the very first leg and ignores all later corrections. - 4 km and 5 km overestimate the distance by adding multiple legs instead of computing net displacement. Common Pitfalls: Typical errors include turning in the wrong direction when interpreting "left" or "right", and adding distances walked instead of calculating net displacement. Learners may also forget that returning along a similar path cancels some earlier movement. Drawing a simple diagram with arrows after each instruction is an effective way to avoid these mistakes and to cross check mental calculations. Final Answer: Ram is 1 km away from his starting point, directly to the east.

Question 7

Johnson leaves home in his car and drives 15 km towards the north, then 10 km towards the west, then 5 km towards the south, then 8 km towards the east and finally turns right and drives another 10 km. How far and in which direction is he from his s…

Accepted Answer

Introduction / Context: This problem is a multi step direction sense question. Johnson drives in several straight legs, taking turns and changing direction. We must determine both his net distance from the starting point and the final direction of that displacement. Such questions check the ability to track movements carefully and to combine north south and east west components without confusion. Given Data / Assumptions: - Johnson starts from home, taken as the origin. - He drives 15 km towards the north. - Then he drives 10 km towards the west. - Then he turns towards the south and drives 5 km. - Next he turns towards the east and drives 8 km. - Finally, when facing east, he turns right, which means towards the south, and drives 10 km. - We assume flat terrain and standard compass directions. Concept / Approach: We represent Johnson's position on a coordinate plane. North is taken as positive y, south as negative y, east as positive x and west as negative x. Each movement updates either x or y, but not both, because all movements are along cardinal directions. After computing the final coordinates, we determine the straight line displacement from the origin. In this specific path, all vertical movements cancel out, leaving a purely westward horizontal displacement. Step-by-Step Solution: 1. Start at (0, 0). 2. Move 15 km north: position becomes (0, 15). 3. Move 10 km west: position becomes (-10, 15). 4. Move 5 km south: position becomes (-10, 10). 5. Move 8 km east: position becomes (-2, 10). 6. Facing east, a right turn points south; move 10 km south: final position is (-2, 0). 7. The displacement from (0, 0) to (-2, 0) is 2 km towards the west. Verification / Alternative check: Instead of computing each coordinate, we can separate north south and east west movements. The total northward distance is 15 km and the total southward distance is 5 km + 10 km = 15 km, which cancel exactly. Horizontally, Johnson goes 10 km west and 8 km east, leaving 2 km net towards the west. Since all vertical components cancel, the final position must be 2 km directly west of the starting point. A simple sketch with arrows will visually confirm that his path ends on the same east west line as his home but shifted left by 2 km. Why Other Options Are Wrong: - 5 km East assumes net movement towards the east instead of west and ignores the larger initial west movement. - 3 km North and 3 km South incorrectly assume an unbalanced north south component even though these cancel. - 7 km West overestimates the net horizontal difference by misadding or forgetting the 8 km east correction. Common Pitfalls: Learners often make sign errors when adding west and east distances or when handling several vertical legs. Another pitfall is misinterpreting the final right turn when already facing east. Carefully tracking facing direction at each step and separating horizontal and vertical totals usually prevents mistakes. It is helpful to write a small table listing cumulative x and y values after each move. Final Answer: Johnson is 2 km to the west of his starting point.

Question 8

From her house Rimi goes 20 km to the north, then 15 km to the west, then 10 km to the south and finally 15 km to the east. In which direction is she from her house now?

Accepted Answer

Introduction / Context: This problem asks about the final direction of Rimi from her house after she walks in four straight legs in cardinal directions. The focus is on net displacement, not on the total distance she travels. This is a common type of reasoning question that trains candidates to combine movements along north south and east west axes. Given Data / Assumptions: - Rimi starts from her house, treated as the origin. - She moves 20 km towards the north. - Then she turns and moves 15 km towards the west. - Then she moves 10 km towards the south. - Finally she moves 15 km towards the east. - Directions are standard compass directions on a flat plane. Concept / Approach: Because all movements are along cardinal directions, we can treat them as changes in horizontal and vertical coordinates. The key idea is that movements in opposite directions partially or fully cancel each other. We therefore compute net movement in the north south axis and in the east west axis. The nonzero net component determines the final direction with respect to the starting point. Step-by-Step Solution: 1. Start at coordinate (0, 0). 2. Move 20 km north: position becomes (0, 20). 3. Move 15 km west: position becomes (-15, 20). 4. Move 10 km south: position becomes (-15, 10). 5. Move 15 km east: position becomes (0, 10). 6. Comparing (0, 10) with (0, 0), she is 10 km north of the starting point with no east west displacement. Verification / Alternative check: We can verify quickly by separate totals. Vertically, total northward movement is 20 km and total southward movement is 10 km, leaving 10 km net to the north. Horizontally, 15 km west and 15 km east cancel completely, giving zero net horizontal movement. A rough sketch as a rectangle up 20, left 15, down 10 and right 15 shows that the path ends directly above the starting position on the same vertical line. This confirms that Rimi is simply to the north of her house. Why Other Options Are Wrong: - South is incorrect because the northward travel is greater than the southward travel. - East and West are wrong because the 15 km west and 15 km east completely cancel. - South East would imply a downward and rightward shift, which does not happen here. Common Pitfalls: A common mistake is to add all distances and then try to infer a direction, instead of computing net movement along each axis. Another error is forgetting that equal distances in opposite horizontal directions cancel each other. Staying organized by writing separate sums for north and south, and for east and west, makes these problems straightforward even under exam pressure. Final Answer: Rimi is to the north of her house after completing the described path.

Question 9

Anu and Bittu start from the same point. Anu walks 35 m towards the south, then 15 m towards the west and then 45 m towards the north. At the same time, Bittu walks 25 m towards the north and then 15 m towards the west. Where is Bittu now with respe…

Accepted Answer

Introduction / Context: This is a comparative direction sense question involving two people, Anu and Bittu, who start from the same point but walk in different directions and distances. The goal is not to find their distance from the starting point but rather the relative position of Bittu with respect to Anu when both have finished walking. Such questions are common in reasoning exams and require careful tracking of coordinates for each person. Given Data / Assumptions: - Both Anu and Bittu start from the same origin point. - Anu walks 35 m south, then 15 m west and then 45 m north. - Bittu walks 25 m north and then 15 m west. - Directions follow the usual north, south, east and west convention. - We assume they walk on straight paths without curves. Concept / Approach: We treat the starting point as (0, 0) and calculate final coordinates for Anu and Bittu separately. South is treated as negative y and north as positive y. West is treated as negative x and east as positive x. After obtaining both final coordinates, we subtract Anu's position from Bittu's position to find how far and in which direction Bittu is from Anu. This relative position answers the question. Step-by-Step Solution: 1. Anu: start at (0, 0), walk 35 m south to (0, -35). 2. Anu then walks 15 m west, reaching (-15, -35). 3. Anu then walks 45 m north, moving to (-15, 10) because -35 + 45 = 10. 4. Bittu: start at (0, 0), walk 25 m north to (0, 25). 5. Bittu then walks 15 m west, reaching (-15, 25). 6. Anu is at (-15, 10) and Bittu is at (-15, 25). Their x coordinates are identical, so they are on the same north south line. 7. The difference in y coordinates is 25 - 10 = 15 m, with Bittu higher (further north). Verification / Alternative check: A quick sketch helps. Draw Anu going down 35 m, left 15 m and then up 45 m, ending 10 m above the horizontal axis. Draw Bittu from the same start going up 25 m and left 15 m, ending further up. Both final points lie on the vertical line x = -15 m. The vertical separation between them is clearly 15 m, with Bittu above Anu. This geometric visualization supports the coordinate calculation. Why Other Options Are Wrong: - Bittu 15 m to the south of Anu reverses the correct north south relationship. - Bittu 95 m to the north or 95 m to the south greatly overstates the separation and does not match the coordinate difference. - Bittu at the same position as Anu is impossible because their y coordinates differ significantly. Common Pitfalls: Students often forget that both paths share the same westward shift of 15 m, which cancels when comparing relative position and leaves only a vertical difference. Confusing relative direction with direction from the starting point is another common problem. Always calculate final coordinates for each person and then compare them to obtain relative position. Final Answer: Bittu is 15 m to the north of Anu.

Question 10

A truck travels 36 km towards the north, then turns towards the west and travels 9 km, then turns towards the south and travels 50 km, and finally turns to its left and travels 9 km. Where is the truck now with reference to its starting position?

Accepted Answer

Introduction / Context: This question describes the path of a truck making several turns and movements in north, west, south and east directions. We are asked to find the truck's final position relative to the starting point, expressed as a direction and distance. The problem demonstrates how combining movements that partly cancel can lead to a simple net displacement even when the path itself is long. Given Data / Assumptions: - The truck first travels 36 km towards the north. - It then turns towards the west and travels 9 km. - It then turns towards the south and travels 50 km. - Finally it turns to its left. When facing south, a left turn points towards the east, and it travels 9 km. - We treat the starting point as the origin on a flat coordinate plane. Concept / Approach: We again use a coordinate approach with north as positive y, south as negative y, east as positive x and west as negative x. Movements west and east affect x, while movements north and south affect y. The key idea is that equal and opposite movements along the same axis cancel. Here, the westward and eastward legs are equal, so the net horizontal movement is zero, while the northward and southward legs differ, leaving a net southward displacement. Step-by-Step Solution: 1. Start at (0, 0). 2. Move 36 km north: new position is (0, 36). 3. Move 9 km west: new position is (-9, 36). 4. Move 50 km south: new position is (-9, -14) because 36 - 50 = -14. 5. Facing south, turn left to face east and move 9 km: final position is (0, -14). 6. From (0, 0) to (0, -14) the displacement is 14 km towards the south. Verification / Alternative check: We can simplify by net sums. Total northward travel is 36 km. Total southward travel is 50 km. The net southward movement is therefore 50 - 36 = 14 km. For east west, the truck goes 9 km west and later 9 km east, which cancel out, giving net zero horizontal movement. So the truck ends directly south of the starting point at a distance of 14 km. A quick sketch shows an up, left, down, and right pattern ending directly below the origin. Why Other Options Are Wrong: - 14 km North reverses the correct vertical direction; the southward distance is larger. - 86 km South and 86 km North come from adding north and south distances without cancellation. - Back at the starting point would require both vertical and horizontal nets to be zero, which is not the case. Common Pitfalls: One frequent mistake is forgetting to change orientation correctly when turning left from south to east. Another is summing all distances and thinking that a larger total means a larger displacement. Carefully separating net movement along each axis and treating opposite directions as positive and negative avoids such errors. Drawing arrows on a simple grid is an excellent way to reinforce understanding in exam conditions. Final Answer: The truck is 14 km to the south of its starting point.

Question 11

A and B start from the same point. A cycles 10 km towards the south and then turns right and cycles 9 km. B cycles 2 km towards the north, then turns left and cycles 15 km and finally turns left again and cycles 12 km. Where is B with respect to A n…

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Introduction / Context: This question compares the final positions of two cyclists, A and B, who start from the same point but follow different routes. The goal is to find where B is located relative to A after all movements. It combines direction sense, relative position and basic coordinate reasoning, which are often tested in competitive examinations. Given Data / Assumptions: - A cycles 10 km towards the south. - A then turns right from facing south, which means towards the west, and cycles 9 km. - B cycles 2 km towards the north. - B then turns left from facing north, which means towards the west, and cycles 15 km. - B again turns left from facing west, which means towards the south, and cycles 12 km. - Both start from the same origin on a flat plane. Concept / Approach: We treat the starting point as (0, 0). Using the standard convention, north is positive y, south is negative y, east is positive x and west is negative x. We compute the final coordinates of A and B separately by updating x and y for each leg. After that, we subtract A's coordinates from B's coordinates to find B's relative position. The sign and magnitude of the difference tell us the direction and distance from A. Step-by-Step Solution: 1. A: start at (0, 0), move 10 km south to (0, -10). 2. A turns right from south to west and moves 9 km: A ends at (-9, -10). 3. B: start at (0, 0), move 2 km north to (0, 2). 4. B turns left from north to west and moves 15 km: B reaches (-15, 2). 5. B then turns left from west to south and moves 12 km: B ends at (-15, -10). 6. Final coordinates: A at (-9, -10) and B at (-15, -10). 7. The y coordinates are equal, but B's x coordinate is 6 units less, so B is 6 km further west than A. Verification / Alternative check: We can reason without full coordinates by focusing on relative motion. Both A and B ultimately reach the same south level of -10 km relative to the start because A goes 10 south and B goes 2 north then 12 south (net 10 south). Horizontally, A goes 9 km west from the original vertical line, while B goes 15 km west. The difference between 15 and 9 is 6, so B is 6 km further to the west than A. A simple sketch with parallel horizontal lines confirms this relationship. Why Other Options Are Wrong: - 6 km East of A reverses the actual direction; B is further west, not east. - 24 km West or East misinterpret the sums of legs and do not match the correct horizontal difference of 6 km. - Directly north of A would require different y coordinates, but both share the same y value. Common Pitfalls: Learners often get confused by multiple turns and may misidentify the new facing direction after each turn. Another pitfall is to compare each person's position with the origin separately instead of directly comparing A and B. Writing down the facing direction after each turn and calculating net north south and east west movements systematically avoids such confusion. Final Answer: B is 6 km to the west of A.

Question 12

A street seller starts from his home and pushes his cart 1 km towards the east, then turns towards the north and walks 4 km, then turns towards the west and walks 9 km and finally turns to his left and walks 4 km. Where is he with respect to his hom…

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Introduction / Context: This question tracks the path of a street seller who starts from his home and walks in a rectangular pattern. We are asked for his final position relative to his home, specifically in terms of direction and distance. The situation is a straightforward application of net horizontal and vertical displacement where some legs cancel each other. Given Data / Assumptions: - He starts from home at an origin point. - First he walks 1 km east. - Then he walks 4 km north. - Then he walks 9 km west. - Finally he turns left from facing west, which means he faces south, and walks 4 km. - Movements are along straight lines on level ground. Concept / Approach: We interpret the movements using a coordinate system with east as positive x and north as positive y. The key observation here is that the northward and southward legs are equal and cancel, leaving only a net horizontal displacement. We compute the net horizontal movement by subtracting eastward distance from westward distance, which directly gives the displacement from home. Step-by-Step Solution: 1. Start at (0, 0) representing the home. 2. Move 1 km east to reach (1, 0). 3. Move 4 km north to reach (1, 4). 4. Move 9 km west to reach (-8, 4) because 1 - 9 = -8. 5. Facing west, turn left to face south and move 4 km to reach (-8, 0). 6. The final position (-8, 0) is 8 km west of the origin (0, 0). Verification / Alternative check: Compute net movements directly. Horizontally, the seller walks 1 km east and 9 km west. Net movement equals 9 - 1 = 8 km west. Vertically, he walks 4 km north and 4 km south, so those movements cancel out completely, leaving zero net vertical movement. A rectangle drawn with up and down sides of equal length visually confirms that he ends up directly west of the home by 8 km. Why Other Options Are Wrong: - 10 km West of his home overestimates the net horizontal displacement; the net is only 8 km. - 8 km East and 10 km East assume he ended up on the opposite side of the origin. - Back at his home would require net horizontal and vertical displacements to be zero, which they are not. Common Pitfalls: Some candidates may misinterpret the final left turn, forgetting that turning left from facing west leads south, not north. Others may forget to subtract eastward movement from westward movement and instead simply add distances. Keeping track of facing direction at each step and writing separate totals for east, west, north and south helps avoid these mistakes. Final Answer: The street seller is 8 km west of his home.

Question 13

Gurpreet is initially facing towards the south. She turns right and walks 35 m, then turns right again and walks 40 m and finally turns left and walks 30 m. In which direction is she facing now?

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Introduction / Context: Unlike previous questions that ask for distance from the starting point, this problem focuses only on the final facing direction of Gurpreet after a sequence of right and left turns. It is a pure orientation question that checks understanding of how directions change when someone initially faces a given direction and then turns right or left by ninety degrees. Given Data / Assumptions: - Gurpreet starts by facing south. - She turns right and walks 35 m. - She then turns right again and walks 40 m. - She finally turns left and walks 30 m. - Each turn is assumed to be exactly 90 degrees. Concept / Approach: The key idea is to track facing direction rather than coordinates. A right turn shifts the facing direction clockwise by 90 degrees, while a left turn shifts it anticlockwise by 90 degrees. Since distance does not affect the direction someone faces, we only need to follow the sequence of turns from the initial orientation. This approach avoids unnecessary coordinate calculations. Step-by-Step Solution: 1. Initial orientation: facing south. 2. First move: she turns right from south. A right turn from south points west. 3. She walks 35 m, but distance does not change the direction she faces, which remains west. 4. Second move: from facing west, she turns right again. A right turn from west points north. 5. She walks 40 m, still facing north at the end of that leg. 6. Third move: from facing north, she turns left. A left turn from north points west. 7. She walks 30 m, and at the end of this movement she is facing west. Verification / Alternative check: We can summarize the turns numerically. Starting from south, a right turn moves us clockwise to west, a second right turn moves us from west to north, and a left turn moves us anticlockwise from north back to west. Ignoring distances, the net effect of the sequence (right, right, left) from south leaves us facing west. A quick diagram of a compass and arrows for each turn confirms this logic. Why Other Options Are Wrong: - South would require a complete loop or a different combination of turns that bring her back to the original orientation. - East never occurs in this sequence of right and left turns starting from south. - North is the direction after the second turn but before the final left turn, not at the end. - North West suggests a diagonal direction, but all turns are exact right angles leading to cardinal directions only. Common Pitfalls: A typical mistake is to imagine facing north initially instead of south or to reverse the meaning of right and left when mentally simulating the turns. Some students also mistakenly think distance influences the facing direction. Concentrating solely on the sequence of right and left turns and using a small sketch of a compass rose helps avoid errors. Final Answer: Gurpreet is finally facing west.

Question 14

Point A is to the south-east of point B. In which direction is point B with respect to point A?

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Introduction / Context: This is a simple conceptual question about opposite directions on the compass. We are told the relative position of point A with respect to point B and asked to reverse the perspective and describe where B lies with respect to A. Such questions test understanding of how opposite diagonal directions relate to each other on a compass. Given Data / Assumptions: - Point A is located to the south east of point B. - South east means A is both south and east of B. - We must state where B is relative to A. - Directions are standard: north, south, east, west, and the four diagonals. Concept / Approach: If A is south east of B, then from B you move downwards (south) and to the right (east) to reach A. To reverse the viewpoint, we imagine standing at A and asking in which diagonal we must look to see B. The reverse of south is north and the reverse of east is west. Therefore, the opposite diagonal to south east is north west. This reasoning relies on the symmetry of the compass and the idea that relative positions are reversible by switching to opposite directions. Step-by-Step Solution: 1. Take B as the reference. A is described as lying to the south east of B. 2. South east combines the south and east directions; so A is below and to the right of B on a standard map. 3. Now take A as the reference point and imagine where B must be relative to A. 4. To move from A to B, we must undo the previous movement. Instead of going south and east, we go north and west. 5. North plus west together give the diagonal direction north west. 6. Therefore, B is to the north west of A. Verification / Alternative check: Draw a simple coordinate system. Place B at the origin (0, 0). Represent A at some coordinates (1, -1) where the positive x axis is east and the positive y axis is north. From B, A is at south east. From A, B is at (-1, 1), which clearly points to the north west. This small diagram confirms the mental reasoning about opposite diagonals without relying on algebraic formulas. Why Other Options Are Wrong: - South West would place B below and to the left of A, which does not match the given relation. - North East would correspond to A being south west of B, not south east. - South East repeats the original direction but in the wrong sense; it is the direction from B to A, not from A to B. - Directly South ignores the east west component and is incomplete for a diagonal relationship. Common Pitfalls: Students sometimes forget that reversing relative position means flipping both components of a diagonal direction, not just one. Another mistake is to think that if A is south east of B then B must also be south east of A, which is incorrect. Always consider that moving from A to B uses opposite directions compared to moving from B to A. Final Answer: Point B is to the north west of point A.

Question 15

Mr. X starts from point A, travels 80 km towards the west, then takes a left turn, travels 50 km and reaches point B. What is the shortest straight line distance between points A and B?

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Introduction / Context: This problem converts a path with a turn into a right triangle and asks for the shortest distance between the starting point A and the final point B. Mr. X travels west and then south (after a left turn from west). The straight line joining A and B is the hypotenuse of a right angled triangle. Such questions link direction sense with basic Pythagoras theorem and distance calculation. Given Data / Assumptions: - Mr. X starts from point A. - He travels 80 km towards the west. - From there he takes a left turn. When facing west, a left turn points towards the south. - He then travels 50 km south and reaches point B. - The ground is flat and distances are measured along straight lines. Concept / Approach: The two legs of travel form perpendicular sides of a right triangle: one horizontal (west) and one vertical (south). The shortest straight line distance from A to B is the hypotenuse of this right triangle. If one side has length a and the other has length b, the hypotenuse is sqrt(a^2 + b^2). Here, a = 80 and b = 50. We compute c = sqrt(80^2 + 50^2) and then simplify the square root to match the options written in the form 10 * sqrt(n). Step-by-Step Solution: 1. Represent A as (0, 0). 2. After travelling 80 km west, Mr. X reaches (-80, 0). 3. Facing west, a left turn points south, so he travels 50 km south to (-80, -50), which is point B. 4. The horizontal difference between A and B is 80 km and the vertical difference is 50 km. 5. The shortest straight line distance AB is given by distance = sqrt(80^2 + 50^2). 6. Compute 80^2 = 6400 and 50^2 = 2500, so distance^2 = 6400 + 2500 = 8900. 7. Therefore distance = sqrt(8900) = sqrt(89 * 100) = 10 * sqrt(89) km. Verification / Alternative check: We can cross check by comparing with the options. The options are of the form 10 * sqrt(n). We know that the hypotenuse must be greater than the longer side but less than the sum of both legs: 80 km < AB < 130 km. Evaluating the approximate values, 10 * sqrt(89) is about 10 * 9.43 ≈ 94.3 km, which fits within this range. The other options correspond to different sums of squares and would not equal 8900 when squared. Since only 10 * sqrt(89) km satisfies the exact calculation, it must be the correct choice. Why Other Options Are Wrong: - 10 * sqrt(39) km would give distance^2 = 3900, which is far less than the required 8900. - 10 * sqrt(98) km corresponds to distance^2 = 9800, not equal to 80^2 + 50^2. - 10 * sqrt(93) km corresponds to distance^2 = 9300, which again does not match 8900. - 50 km is merely one leg of the triangle and not the combined hypotenuse. Common Pitfalls: Common mistakes include adding the distances (80 + 50) instead of using the Pythagoras theorem, or squaring and adding incorrectly. Some test takers also misinterpret the left turn direction from west. Always confirm that the two legs are perpendicular and then apply distance = sqrt(a^2 + b^2). Checking approximate values of square roots can provide a quick sanity check against unreasonable answers. Final Answer: The shortest distance between points A and B is 10 * sqrt(89) km.

Question 16

After their day's work two village women return home from the same starting point. The first woman walks 1.5 km towards the west and then turns right and walks 3 km to reach her house. The second woman walks 1 km towards the north, then turns east a…

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Introduction / Context: This question describes the final positions of two women returning home from a common starting point after their day's work. We are asked to locate the first woman's house with respect to the second woman's house. The problem involves calculating coordinates for each house and then determining the relative horizontal distance and direction between them. Given Data / Assumptions: - Both women start from the same origin point. - First woman: walks 1.5 km west, then turns right from west (towards north) and walks 3 km to her house. - Second woman: walks 1 km north, then turns east and walks 3.5 km, then turns left from east (towards north) and walks 2 km to her house. - All movements are along straight segments with right angle turns. Concept / Approach: We place the starting point at coordinate (0, 0) and use a standard coordinate system: east as positive x, north as positive y. For each woman, we track the final coordinates by incrementing or decrementing x and y according to each described move. To find where the first woman's house is with respect to the second's, we compute the vector from the second house to the first house. The sign of this difference tells us the direction (east or west), and the magnitude tells us the distance. Step-by-Step Solution: 1. First woman: start at (0, 0) and go 1.5 km west: position (-1.5, 0). 2. From facing west, a right turn means north. She walks 3 km north: first house at (-1.5, 3). 3. Second woman: start at (0, 0) and walk 1 km north: position (0, 1). 4. She turns east and walks 3.5 km: position (3.5, 1). 5. From facing east, a left turn means north. She walks 2 km north: second house at (3.5, 3). 6. To find the first house relative to the second, subtract coordinates: (-1.5, 3) minus (3.5, 3) = (-5, 0). 7. The result (-5, 0) means the first house is 5 km directly west of the second house. Verification / Alternative check: The vertical coordinates of both houses are equal (y = 3 km). This shows they lie on the same east west line. Horizontally, the first house is 1.5 km west of the origin, while the second house is 3.5 km east of the origin. The separation between them is 1.5 + 3.5 = 5 km. Since the first is on the west side and the second on the east side, the first must be located 5 km west of the second. A diagram with both paths drawn from the common starting point visually confirms this reasoning. Why Other Options Are Wrong: - 2 km west or 2 km east underestimate the horizontal gap and do not match the coordinate difference. - 5 km east reverses the correct direction; the first house is to the west, not east, of the second. - At the same location ignores the clear horizontal separation between the coordinates. Common Pitfalls: Candidates may misinterpret right and left turns relative to the current facing direction rather than the compass, leading to incorrect final coordinates. Another error is to compare each house with the origin instead of directly comparing the two houses. Being systematic in tracking coordinates and carefully interpreting right and left from the walker's perspective is essential to avoid such mistakes. Final Answer: The first woman's house is 5 km west of the second woman's house.

Question 17

Raj is facing north. He cycles 8 km towards the north, then moves 10 km in the south-east direction and finally 6 km towards the west. In which direction is he from his original position now?

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Introduction / Context: This problem combines straight northward motion, a diagonal motion towards the south east, and a final straight westward motion. We are asked only for Raj's final direction relative to his starting point, not the exact distance. The diagonal component makes the motion two dimensional and requires careful handling of both horizontal and vertical movements. Given Data / Assumptions: - Raj starts from an original position facing north. - He cycles 8 km towards the north. - He then moves 10 km towards the south east. - Finally he moves 6 km towards the west. - South east is a diagonal direction halfway between south and east, making a 45 degree angle with each axis. Concept / Approach: We use a coordinate system where east is positive x and north is positive y. Northward and westward segments are easy to represent, while the south east movement must be broken into equal horizontal and vertical components because it is at 45 degrees. By summing all x components and all y components, we obtain the final coordinate. The signs of the resulting x and y tell us the final direction: positive x and positive y mean north east, and so on. Step-by-Step Solution: 1. Start at (0, 0). 2. Move 8 km north: new position is (0, 8). 3. Move 10 km south east. At 45 degrees, the components are 10 / sqrt(2) km east and 10 / sqrt(2) km south. 4. Numerically, 10 / sqrt(2) is about 7.07 km. Adding components, x becomes 0 + 7.07 = 7.07 and y becomes 8 - 7.07 ≈ 0.93. 5. Move 6 km west: subtract 6 from the x coordinate. New x = 7.07 - 6 = 1.07, y remains about 0.93. 6. Final position is approximately (1.07, 0.93). Both coordinates are positive, so Raj is to the east and north of the starting point. 7. Since both x and y are positive, his final direction from the origin is north east. Verification / Alternative check: Even without exact decimals, we know that the south east move reduces some of the northward distance and introduces eastward displacement. After 8 km north, moving approximately 7.07 km south reduces the net north movement to around 0.93 km. The same diagonal leg adds about 7.07 km east. Subtracting the 6 km west leaves about 1.07 km east. Having a small net north and a small net east displacement shows that Raj is in the north east quadrant relative to the start. A rough scaled diagram of the three legs confirms that the endpoint lies slightly north and slightly east of the origin. Why Other Options Are Wrong: - South East would require the final y coordinate to be negative, which it is not. - North West would require the x coordinate to be negative, which contradicts the final positive x value. - South West would require both x and y to be negative, which is not the case. - At the original position would mean both net x and net y are zero, which they clearly are not after unequal movements. Common Pitfalls: A frequent error is treating the 10 km south east leg as 10 km purely south or purely east instead of splitting it into components. Another mistake is to subtract 6 km west directly from 10 km south east without considering that the diagonal leg already included an east component. Carefully separating movements into x and y components and checking signs ensures correct classification of the final direction. Final Answer: Raj is to the north east of his original position.

Question 18

Study the following information and answer the question. Point A is 8 m to the west of point B. Point C is 4 m to the south of point B. Point D is 4 m to the east of point C. Point F is 6 m to the north of point D. Point E is 8 m to the west of poin…

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Introduction / Context: This is a grid based direction question describing several points located relative to one another. Instead of people walking, we have fixed points with given distances in metres. The task is to determine the straight line distance between two specific points, H and D, after interpreting all given positional relationships correctly. This tests diagram drawing, coordinate reasoning and attention to detail. Given Data / Assumptions: - Point A is 8 m west of point B. - Point C is 4 m south of point B. - Point D is 4 m east of point C. - Point F is 6 m north of point D. - Point E is 8 m west of point F. - Point G is 2 m south of point E. - Point G is 4 m north of point H, so H is 4 m south of G. Concept / Approach: The easiest method is to place one point at the origin of a coordinate system and compute coordinates for all other points by following the given directions. Once we have coordinates for H and D, we compute the distance between them. In this particular construction, H and D turn out to lie horizontally apart on the same east west line, so their distance is simply the absolute difference in their x coordinates. Step-by-Step Solution: 1. Place point B at (0, 0) for convenience. 2. Point A is 8 m west of B, so A is at (-8, 0). 3. Point C is 4 m south of B, so C is at (0, -4). 4. Point D is 4 m east of C, so D is at (4, -4). 5. Point F is 6 m north of D, so F is at (4, 2). 6. Point E is 8 m west of F, so E is at (-4, 2). 7. Point G is 2 m south of E, so G is at (-4, 0). 8. G is 4 m north of H, so H must be 4 m south of G, at (-4, -4). 9. Thus H is at (-4, -4) and D is at (4, -4). They share the same y coordinate. 10. The distance between H and D is the difference in x coordinates: 4 - (-4) = 8 m. Verification / Alternative check: A sketch on graph paper confirms these coordinates. B at the centre, C directly below, D further right, F above D, E to the left of F, and G below E create a closed shape. Dropping 4 m from G to H lines H exactly below G and on the same horizontal level as C and D. Counting horizontal squares between H and D gives 8 m. Since there is no vertical separation, the straight line distance is simply this horizontal gap. Why Other Options Are Wrong: - 11 m or 10 m would require a diagonal separation or different coordinates, which the detailed construction does not support. - 6 m or 4 m underestimate the actual horizontal spacing between H and D. - Only 8 m matches the coordinate difference and the diagram. Common Pitfalls: One common error is mixing up east and west or forgetting that each new point is placed relative to the last defined point, not necessarily the origin. Another pitfall is misplacing H by moving it relative to the wrong point instead of G. Working step by step, writing coordinates and using a rough sketch minimizes the chance of such mistakes and makes the final calculation straightforward. Final Answer: The distance between points H and D is 8 m.

Question 19

In the morning X and Y are walking towards each other in a park. When they meet, Y's shadow falls straight in front of X along the line joining them. In which direction is X facing?

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Introduction / Context: This question involves understanding the relationship between the sun's position, the direction of a person's shadow and the facing direction of another person. X and Y are walking towards each other in the morning, and Y's shadow falls straight in front of X. We must deduce X's facing direction using basic facts about how shadows are cast. Given Data / Assumptions: - It is morning, so the sun is in the eastern part of the sky. - X and Y are walking towards each other along a straight path in a park. - When they meet, Y's shadow falls straight in front of X along the same line on which they are walking. - Shadows are cast in the direction opposite to the sun. Concept / Approach: In the morning the sun is roughly in the east, so shadows fall towards the west. If Y's shadow falls straight in front of X, that means the line from Y to the tip of Y's shadow runs directly towards X. Therefore, X must be located in the direction where Y's shadow points. Since Y's shadow points west in the morning, X must be to the west of Y when they meet. Because they are walking towards each other, X must be facing east and Y must be facing west at the moment of meeting. Step-by-Step Solution: 1. In the morning, the sun is in the east, so for any standing person, the shadow will fall towards the west. 2. At the moment X and Y meet, Y's shadow is said to fall straight in front of X along the line on which they are walking. 3. This means that from Y, the direction of the shadow passes through X or lies directly between Y and X. 4. Because the shadow points west, X must be towards the west of Y, standing on the same line. 5. Since X and Y are walking towards each other, if X is to the west of Y, X must be facing east and Y must be facing west. 6. Therefore, X is facing east at the time when Y's shadow falls straight in front of him. Verification / Alternative check: Visualize a straight path running east to west. Place X at a point on the west side and Y at a point on the east side, walking towards each other. In the morning, light travels from east to west, so Y's shadow extends behind him towards the west, that is, towards X. When they meet, Y's shadow falls between Y and X, effectively in front of X as he looks eastwards. Trying the opposite configuration, with X on the east and Y on the west, would produce shadows pointing away from X rather than towards him, so that setup does not satisfy the problem statement. Why Other Options Are Wrong: - South or North do not align with the east to west shadow pattern in the morning. - West would place X facing towards the west, making it impossible for Y's westward shadow to fall in front of him along the line of approach. - North East is a diagonal direction that does not fit the simple east west shadow logic provided. Common Pitfalls: Examinees sometimes mix up the sun's position at different times of day, or they imagine shadows incorrectly. Remembering that in the morning the sun is in the east and shadows fall towards the west is crucial. Another pitfall is forgetting that they are walking towards each other, which constrains their relative positions on the line. Ensuring consistency between the movement direction and the shadow direction avoids wrong conclusions. Final Answer: X is facing east.

Question 20

A man moves towards the east and then takes a left turn. After covering some distance in that direction, he takes a right turn and finally takes another right turn. Which direction is the man facing now?

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Introduction / Context: This question deals only with the facing direction of a man after a sequence of right and left turns, starting from an initial direction. The distances covered are irrelevant to the final facing direction, so we focus entirely on how each turn changes his orientation. This is a standard type of reasoning question that tests mental rotation of directions. Given Data / Assumptions: - Initially the man is moving towards the east. - He takes a left turn and continues in that new direction. - After some distance he takes a right turn. - Finally he takes another right turn. - All turns are 90 degree turns. Concept / Approach: We track only orientation, not position. From east, left means turning north, and right means turning south. Each new right or left is interpreted relative to the current facing direction. The easiest method is to imagine standing at a fixed point and turning as described. Alternatively, we can think in terms of compass directions and apply right or left rotations step by step until the final orientation is clear. Step-by-Step Solution: 1. Starting direction: east. 2. First turn: left from east takes him to facing north. 3. He walks some distance facing north, but direction remains north. 4. Second turn: right from north takes him to facing east again. 5. He walks further while facing east. 6. Third turn: right from east takes him to facing south. 7. At the end of the sequence of turns he is therefore facing south. Verification / Alternative check: We can mark the sequence on a small compass diagram. Draw arrows in this order: east, then a left arrow that points north, then a right arrow that points east again, and then a right arrow from east that points south. Because the distances do not affect orientation, this sketch directly shows the correct final direction. Trying to assign coordinates would be unnecessarily complicated, as only rotation matters. Why Other Options Are Wrong: - West is two right turns away from north, which does not match the given left, right, right pattern from east. - East is the direction just before the final right turn, not after it. - North is the direction after the first left turn, not the final direction. - South West is a diagonal direction, but all turns are at right angles between cardinal directions only. Common Pitfalls: Students sometimes misapply left and right because they mentally flip orientation as if observing from above rather than standing in the man's shoes. Always imagine you are facing the current direction and then mentally rotate to the left or right from your own viewpoint. Writing the sequence of directions in order can also prevent confusion in multi step turn problems. Final Answer: The man is finally facing south.

Direction Sense Test Questions