Question 1

Punit starts from point R and walks straight 10 km towards the west, then turns right and walks 12 km, and again turns right and walks straight 7 km. In which direction is Punit now located with respect to point R?

Accepted Answer

Introduction / Context: This direction sense question requires determining the final direction of a person from his starting point after a few straight movements and right angle turns. Punit starts at point R, walks west, then turns right twice and walks given distances. We are asked for his direction from point R, not the exact distance. This involves combining horizontal and vertical displacements to see which quadrant his final position occupies. Given Data / Assumptions: Punit starts at point R. He walks 10 km west from R. He turns right and walks 12 km. He turns right again and walks 7 km. All turns are right angle turns, with no diagonal movement. We interpret right turns as clockwise 90 degree rotations from the current facing direction. Concept / Approach: We can track Punit's path using coordinates. By setting point R at the origin and marking western movement as negative x and northern movement as positive y, each leg of his path can be recorded as a change in coordinates. Right turns are interpreted based on the direction he is facing at that moment. Once we know his final coordinates, we can infer whether he lies to the north, south, east, or west of R, and thus identify the final direction such as north west or south east. Step-by-Step Solution: Step 1: Place point R at (0, 0).Step 2: Punit walks 10 km west, so his new position is (−10, 0), and he is facing west.Step 3: A right turn from west means he now faces north. Walking 12 km north takes him to (−10, 12).Step 4: Another right turn from north means he now faces east. Walking 7 km east takes him to (−3, 12).Step 5: His final coordinates relative to R are (−3, 12). This means he is 3 km west and 12 km north of point R.Step 6: Being both west and north of R places him in the north west direction relative to R. Verification / Alternative check: A sketch of the path confirms this conclusion. From R, draw a horizontal segment 10 km to the left to represent the first leg. Then draw a vertical segment 12 km upward to show the second leg. Finally, draw a horizontal segment 7 km to the right for the third leg. The end point clearly lies above and slightly to the left of R. This visual inspection confirms that Punit is north west of R and not in any other quadrant. Why Other Options Are Wrong: North east would require him to be east of R as well as north, which contradicts the fact that his x coordinate is negative. South east and south west would place him below R in the diagram, but his y coordinate is positive, indicating a position north of R. Pure east would require the x coordinate to be positive and y to be zero, which is not the case. Only the north west direction fits the sign pattern of his final coordinates. Common Pitfalls: Some candidates mistakenly treat both right turns as turning towards the south after the first leg, which changes the orientation of the path entirely. Others forget that a right turn from west leads to north, not south. It is very helpful to draw the four directions and indicate facing direction at each stage to avoid such misinterpretations. Keeping track of coordinates instead of relying only on verbal descriptions makes the reasoning much more solid. Final Answer: From point R, Punit's final position lies in the North-West direction.

Question 2

Starting from his home, a boy rides his bike 8 km towards the west, then takes a left turn and travels 10 km. From there, he turns 180 degrees in the clockwise direction and travels another 16 km. Finally, he takes a right turn and travels 8 km more…

Accepted Answer

Introduction / Context: This problem describes a boy riding his bike in several legs, making left and right turns and one 180 degree turn. We must determine his final distance and direction from his home, which is his starting point. Direction sense questions like this require both tracking orientation after each turn and summing up the displacements along the north south and east west directions. Given Data / Assumptions: From home, the boy rides 8 km west. He then takes a left turn and rides 10 km. From this point he turns 180 degrees clockwise and rides another 16 km. Finally he takes a right turn and rides 8 km. All movements are along straight lines in the cardinal directions, and 180 degrees clockwise reverses his direction. Concept / Approach: We start by translating each leg into coordinates. Taking west as negative x, east as positive x, north as positive y, and south as negative y, each movement gives us a change in x and y. Left and right turns are interpreted relative to the direction he is facing at that moment. A 180 degree clockwise turn simply reverses the facing direction. After summing all displacement vectors, we obtain the net displacement from the starting point, whose magnitude and sign determine the final distance and direction. Step-by-Step Solution: Step 1: Let the home position be (0, 0). The boy initially faces west.Step 2: Riding 8 km west takes him to (−8, 0), still facing west.Step 3: From facing west, a left turn takes him to face south. Riding 10 km south takes him to (−8, −10).Step 4: A 180 degree clockwise turn from south reverses his direction to north. Riding 16 km north from (−8, −10) moves him to (−8, 6).Step 5: He is now facing north. A right turn from north takes him to face east. Riding 8 km east from (−8, 6) moves him to (0, 6).Step 6: His final coordinates are (0, 6) relative to his home at (0, 0).Step 7: The net displacement is 6 km north and 0 km east or west, so the distance is 6 km and the direction is north. Verification / Alternative check: We can check the vertical movements alone: he goes 10 km south and then 16 km north, which gives a net 6 km north. For the horizontal movement, he first goes 8 km west and later 8 km east, which cancel exactly, yielding net 0 km in the east west direction. So even without coordinates, we can see that horizontally he returns to the same line as his starting point, but vertically he ends 6 km north of it. This confirms that the final location is 6 km towards the north of his home. Why Other Options Are Wrong: The option 10 km south would require the net vertical displacement to remain negative, which is inconsistent with going 16 km north after 10 km south. The option 12 km west implies an uncancelled 12 km horizontal offset, which is impossible since 8 km west is later countered by 8 km east. The option 6 km east would require a net positive x displacement, but we found the final x coordinate to be zero. The 4 km north west suggestion combines both north and west components and does not fit the exact cancellation of horizontal motion. Common Pitfalls: Common mistakes include misinterpreting the 180 degree clockwise turn and thinking it leads to east instead of north, or forgetting to cancel the equal east and west legs of 8 km each. Another error is to compute total distance travelled rather than net displacement. Focusing on net north south and east west components and recognising when movements cancel each other is crucial for accuracy in such problems. Final Answer: The boy is now located 6 km to the North of his original starting position at home.

Question 3

Anil is facing the east direction. He then turns 90 degrees clockwise and then turns 135 degrees anti clockwise. After making these two turns, in which direction is he now facing?

Accepted Answer

Introduction / Context: This is a straightforward orientation question. Anil initially faces east, then rotates through a right angle clockwise and then through 135 degrees anti clockwise. The task is to find his final facing direction. It tests basic understanding of clockwise and anti clockwise rotations and the layout of the four main directions plus diagonals on a circle. Given Data / Assumptions: Anil starts facing east. He turns 90 degrees clockwise. He then turns 135 degrees anti clockwise. We use a standard compass where north is at 0 degrees, east at 90 degrees, south at 180 degrees, west at 270 degrees, and north east at 45 degrees. Concept / Approach: We can represent directions as angles and treat rotations as additions or subtractions of these angles. Clockwise rotation is taken as increasing the angle from the reference, while anti clockwise rotation is taken as decreasing it, or vice versa, as long as we are consistent. The key is to compute the net angular position after both rotations relative to north and then interpret that angle as a known direction such as north east or west. Step-by-Step Solution: Step 1: Represent east as 90 degrees.Step 2: A 90 degree clockwise turn from east leads to south, which corresponds to 180 degrees.Step 3: From south at 180 degrees, Anil now turns 135 degrees anti clockwise. Subtracting 135 degrees gives 180 − 135 = 45 degrees.Step 4: An angle of 45 degrees is exactly halfway between north (0 degrees) and east (90 degrees), which corresponds to the north east direction.Step 5: Therefore, after both rotations, Anil is facing north east. Verification / Alternative check: We can also reason by directions alone. From east, a 90 degree clockwise turn leads to south. From south, a 90 degree anti clockwise turn leads back to east, and another 45 degrees anti clockwise moves him further towards north, landing at north east. This stepwise reasoning, broken into a 90 degree and a 45 degree anti clockwise component, confirms the angle calculation and supports the conclusion that Anil faces north east at the end. Why Other Options Are Wrong: North would require a total rotation that brings him exactly opposite south, which is not achieved with a 90 clockwise and a 135 anti clockwise turn. West lies opposite east and would involve a 270 degree shift, which does not match the net change here. South west is between south and west, but Anil ends between north and east instead. South east is not possible because he moves away from the southern region in his final anti clockwise rotation. Only north east fits both the numerical angle and the intuitive compass reasoning. Common Pitfalls: Common errors include forgetting to change the sign of the second rotation and adding 90 and 135 in the same direction, or misreading clockwise and anti clockwise. Some learners incorrectly assume that a larger second rotation always dominates without checking the final angle. Using a simple angle representation or drawing the directions as points on a circle and moving step by step around it helps avoid these mistakes. Final Answer: After turning 90 degrees clockwise and then 135 degrees anti clockwise from facing east, Anil is finally facing towards the North-East.

Question 4

A man walks 9 km towards the east and then 12 km towards the south. Taking his starting point as reference, how far is he now from the starting point?

Accepted Answer

Introduction / Context: This is a standard distance calculation question involving perpendicular movements. The man walks first east and then south, creating a right angled path. We need to calculate the straight line distance from his starting point to his final position. This is a direct application of the Pythagorean theorem to a right angled triangle with known legs. Given Data / Assumptions: The man walks 9 km towards the east. He then walks 12 km towards the south. We assume a flat plane with east west and north south directions perpendicular to each other. We are asked for the straight line distance from the starting point to the final point, not the total path length walked. Concept / Approach: The path forms a right angled triangle whose legs are the eastward and southward distances. The hypotenuse of this triangle represents the crow flight distance between the starting and final points. The Pythagorean theorem states that, for a right angled triangle with legs a and b and hypotenuse c, we have c^2 = a^2 + b^2. Substituting a = 9 km and b = 12 km gives a straightforward calculation. Step-by-Step Solution: Step 1: Take the starting point as the origin (0, 0). After walking 9 km east, the man is at (9, 0).Step 2: After walking 12 km south, he is at (9, −12).Step 3: The displacement from the origin to (9, −12) has horizontal component 9 km and vertical component 12 km.Step 4: Apply the Pythagorean theorem: c^2 = 9^2 + 12^2 = 81 + 144 = 225.Step 5: Take the square root: c = √225 = 15 km.Step 6: Therefore, his straight line distance from the starting point is 15 km. Verification / Alternative check: We can notice that (9, 12, 15) is a scaled version of the classic (3, 4, 5) Pythagorean triple, multiplied by 3. In such triples, if the legs are 3 units and 4 units, the hypotenuse is 5 units. Here, the legs are 9 = 3 × 3 and 12 = 3 × 4, so the hypotenuse must be 3 × 5 = 15. This quick check confirms the more formal square and square root calculation and ensures that no arithmetic mistake has been made. Why Other Options Are Wrong: The option 8 km is smaller than both legs of the triangle and cannot be the hypotenuse. The option 6 km is even smaller and clearly impossible. The value 7.5 km might come from averaging the legs or mistakenly dividing something by 2, which is not correct here. The option 9 km corresponds only to the eastward leg and ignores the additional southward displacement. Only 15 km correctly reflects the combined effect of both perpendicular movements. Common Pitfalls: Some students mistakenly add the distances 9 and 12 and choose 21 km, confusing total path length with straight line distance. Others forget to square the numbers and incorrectly add them directly before taking a square root. Another error is to treat the triangle as isosceles or to guess based on rough proportions. Remembering the Pythagorean relationship and the common triples like 3, 4, 5 and their multiples is very helpful in such problems. Final Answer: The man is now at a straight line distance of 15 km from his starting point.

Question 5

Rohan walks a distance of 3 km towards the north, then turns to his left and walks 2 km. He again turns left and walks 3 km. At this point he turns left once more and walks 3 km. How far is he now from the starting point?

Accepted Answer

Introduction / Context: This direction sense question describes Rohan walking along a path with several left turns. The sequence of movements forms a polygonal path, and we must determine his final distance from the starting point. The problem is typical of reasoning tests where tracking left and right turns, along with distances, gradually creates a simple geometric shape such as a rectangle or an offset path. Given Data / Assumptions: Rohan walks 3 km towards the north from his starting point. He turns left and walks 2 km. He again turns left and walks 3 km. He then turns left once more and walks 3 km. All turns are 90 degrees to the left relative to his current facing direction. We are asked only for the straight line distance from his final position to the starting point. Concept / Approach: We place Rohan's movements on a coordinate plane to track his position. A left turn is interpreted as a 90 degree anticlockwise rotation from his current direction. With north as positive y and east as positive x, we can represent each leg of the journey as changes in x and y. After the final leg, the straight line distance is the length of the displacement vector from the origin to his final coordinates, which can be found using simple arithmetic rather than full Pythagorean calculation if the components are small. Step-by-Step Solution: Step 1: Take the starting point as (0, 0). Rohan initially faces north.Step 2: Walking 3 km north moves him to (0, 3), still facing north.Step 3: A left turn from north makes him face west. Walking 2 km west moves him to (−2, 3).Step 4: A left turn from west makes him face south. Walking 3 km south moves him to (−2, 0).Step 5: A left turn from south makes him face east. Walking 3 km east moves him to (1, 0).Step 6: His final coordinates relative to the starting point are (1, 0).Step 7: The straight line distance from the origin to (1, 0) is simply 1 km. Verification / Alternative check: We can also reason geometrically. The first three legs form a rectangle: 3 km up, 2 km left, and 3 km down, bringing him to a point 2 km west of the start along the same horizontal line. The final leg of 3 km east overshoots the starting point by 1 km towards the east, placing him exactly 1 km away from where he began. This visualisation aligns with the coordinate calculation and confirms that the distance is 1 km. Why Other Options Are Wrong: The values 5 km and 4 km are much larger than any small offset created by a slight overshoot on the last leg. The option 3 km might be chosen if someone looks only at the first or third leg and ignores the rest of the movement. The value 2 km corresponds to the width of the rectangle created by the second leg, but the additional final leg changes his position further. Only 1 km correctly reflects the net horizontal displacement from the starting point. Common Pitfalls: A common error is to assume that because Rohan walked 3 km north and later 3 km south, he must be back at the starting point, forgetting that he shifted west in between. Another mistake is to treat left turns as absolute directions instead of relative to his current facing orientation, which can produce a wrong shape. Drawing a simple diagram or writing coordinates for each step helps prevent these logical slips. Final Answer: Rohan is now at a straight line distance of 1 km from his starting point.

Question 6

The distance between two cities is 30 kilometres. A man travels from the first city to the second at a speed of 30 kilometres per hour and returns along the same route at a speed of 20 kilometres per hour. What is his average speed for the entire ro…

Accepted Answer

Introduction / Context: Average speed problems are very common in quantitative aptitude and direction or distance based reasoning questions. In many questions the speed of going from one place to another is different from the speed while returning. The key idea is that the average speed is not the simple average of the two speeds when the distances in the two parts of the journey are the same. This question checks whether the learner remembers the correct formula and can carefully compute the total distance and the total time for a complete round trip between two cities. Given Data / Assumptions: The distance between the two cities is 30 kilometres. The man travels from City A to City B at 30 kilometres per hour. He returns from City B to City A at 20 kilometres per hour. The route and distance on both legs of the journey are the same. We assume there are no breaks, delays or changes in speed within each leg. Concept / Approach: To find average speed over a complete journey, we use the fundamental formula: average speed = total distance travelled / total time taken. When the distance covered in the two parts of the journey is the same but speeds are different, a common shortcut is the harmonic mean: average speed = 2 * x * y / (x + y), where x and y are the speeds. However, it is safer for exam purposes to explicitly calculate total distance and total time and then divide, so that mistakes are less likely. Step-by-Step Solution: Step 1: Distance from the first city to the second city is 30 kilometres. Step 2: The same distance is covered again on the way back, so total distance = 30 + 30 = 60 kilometres. Step 3: Time taken to go from City A to City B at 30 kilometres per hour is time = distance / speed = 30 / 30 = 1 hour. Step 4: Time taken to return from City B to City A at 20 kilometres per hour is time = distance / speed = 30 / 20 = 1.5 hours. Step 5: Total time for the round trip = 1 hour + 1.5 hours = 2.5 hours. Step 6: Average speed for the entire journey = total distance / total time = 60 / 2.5. Step 7: Compute 60 / 2.5. Multiply numerator and denominator by 10 to avoid decimals: (60 * 10) / (2.5 * 10) = 600 / 25 = 24 kilometres per hour. Verification / Alternative check: We can verify using the harmonic mean shortcut for equal distances: average speed = 2 * x * y / (x + y). Here x = 30 and y = 20. So average speed = 2 * 30 * 20 / (30 + 20) = 1200 / 50 = 24 kilometres per hour. This matches the value obtained from the detailed distance and time calculation. Therefore the computed answer is consistent and correct. Why Other Options Are Wrong: Option A, 25 kilometres per hour, is close but incorrect and may come from rough mental estimation rather than proper calculation. Option C, 10 kilometres per hour, is much too low. It may come from confusing speed with time or from incorrect division. Option D, 26 kilometres per hour, is another nearby distractor meant to trap those who miscalculate 60 / 2.5. Option E, 20 kilometres per hour, is simply one of the given speeds and represents a wrong assumption that average speed equals the slower speed. Common Pitfalls: A very common mistake is to take the simple average of the two speeds, that is (30 + 20) / 2 = 25 kilometres per hour. This is incorrect because average speed must always be computed as total distance divided by total time, not the average of the speeds. Another mistake is forgetting that the man travels the same distance twice, so the total distance is 60 kilometres, not 30 kilometres. Some learners also mix up the role of time and speed while dividing, which leads to values such as 10 kilometres per hour or other incorrect numbers. Carefully writing distance, speed and time for each leg prevents these errors. Final Answer: The man covers a total distance of 60 kilometres in 2.5 hours, so his average speed for the entire round trip is 24 kilometres per hour.

Question 7

A girl walks 30 metres towards the south from her starting point. Then, turning to her right, she walks another 30 metres. After that she turns to her left and walks 20 metres. Finally, she turns to her left again and walks 30 metres. How far is she…

Accepted Answer

Introduction / Context: This is a classic direction sense and distance problem. Such questions appear frequently in reasoning sections of competitive examinations. They test spatial imagination, the ability to track right and left turns, and the skill of computing net displacement using simple geometry or coordinate style reasoning. The key objective is to determine how far the girl is from the starting point after several movements in different directions, not the total path length walked. Given Data / Assumptions: The girl starts from an initial point which we can treat as the origin. She first walks 30 metres towards the south. She then turns right from facing south and walks 30 metres. Next she turns left and walks 20 metres. Finally she turns left again and walks 30 metres. All turns are perfect right angles unless specifically stated otherwise. We need the straight line distance between her starting position and her final position. Concept / Approach: The systematic way to solve direction sense questions is to imagine or sketch a coordinate grid. We choose east as the positive x direction and north as the positive y direction. Then we track each movement step by step, updating the coordinates. Right and left turns are interpreted relative to the current facing direction. Once we know the coordinates of the final point, the straight line distance from the origin can be found using the Pythagoras rule: distance = square root of (x^2 + y^2). For simple right angled movements, this usually produces integer distances. Step-by-Step Solution: Step 1: Assume the girl starts at point O with coordinates (0, 0), facing south for the first movement. Step 2: She walks 30 metres south, so her new position is (0, -30). Step 3: From facing south, a right turn means facing west. She walks 30 metres west to reach the point (-30, -30). Step 4: From facing west, a left turn means facing south. She now walks 20 metres south to point (-30, -50). Step 5: From facing south, another left turn means facing east. She walks 30 metres east to point (0, -50). Step 6: The final coordinates are (0, -50). So the horizontal displacement is 0 metres and the vertical displacement is -50 metres. Step 7: The straight line distance from the origin to the final point is therefore the magnitude of the vertical displacement, which is 50 metres. Verification / Alternative check: Instead of working with coordinates, we can track net horizontal and vertical movements. Vertically, she goes 30 metres south and later 20 metres south, with no northward motion, giving a total of 50 metres south. Horizontally, she first goes 30 metres west and later 30 metres east, which cancel out, resulting in zero net horizontal displacement. Hence the final position is exactly 50 metres south of the starting point, so the straight line distance between the two points is 50 metres, confirming the earlier calculation. Why Other Options Are Wrong: Option A, 20 metres, confuses one of the intermediate legs with the overall displacement. Option B, 30 metres, may come from ignoring the 20 metre leg or misreading the path as a simple rectangle. Option D, 60 metres, looks like the sum of 30 and 30, which is incorrect because it ignores cancellation in the horizontal direction. Option E, 40 metres, is a random distractor with no relation to the actual Pythagoras computation for this path. Common Pitfalls: Learners often misinterpret right and left turns when facing different directions. For example, a right turn from south leads to west, not east. Another frequent mistake is to add distances directly rather than computing net displacement. Remember that average or resultant displacement depends on how far you end from where you started, not on the total path walked. Drawing a simple diagram or using coordinates significantly reduces the chance of error in such questions. Final Answer: The girl finishes 50 metres away from her starting point, directly to the south, so the required distance is 50 metres.

Question 8

Study the following information and answer the question. Each of five friends A, B, C, D and E travels a different distance from home to the workplace. B travels 15 kilometres to reach the office. A travels more than B but less than E. D travels mor…

Accepted Answer

Introduction / Context: This verbal reasoning question deals with ordering and inequality relationships among distances travelled by five friends. Instead of exact values for all, we are given partial comparisons such as who travels more than whom and the fact that all distances are distinct. The question aims to test your ability to translate statements into a logical ordering and then deduce which friend could travel a particular distance, in this case 5 kilometres, without contradicting any of the conditions. Given Data / Assumptions: There are five friends: A, B, C, D and E. Each friend travels a different distance to his or her workplace. B travels exactly 15 kilometres. A travels more than B but less than E, so B < A < E. D travels more than only C, so C has the shortest distance and D is the second shortest. The friend who travels the most covers 30 kilometres. All distances are positive and distinct. Concept / Approach: We are essentially arranging five distinct distances in increasing order using inequality information. First, we identify who is definitely smallest or largest based on phrases like "more than only C" and "the one who travels the most". Then we look at the given exact value for B and check where B can fit in the order. Finally we test which person can logically have a distance of 5 kilometres without violating any of the constraints. Reasoning with a model example of distances is often the clearest way to see this. Step-by-Step Solution: Step 1: From the statement that D travels more than only C, we know that C is the shortest and D is the second shortest. Therefore the increasing order of distances starts with C, then D, followed by three others. Step 2: B, A and E must therefore travel further than D. Symbolically we have: C < D < B, A, E (in some order). Step 3: We also know that A travels more than B but less than E, so B < A < E. Combining, the full order from smallest to largest is: C < D < B < A < E. Step 4: The largest distance is 30 kilometres. The only candidate that can take this maximum role in the chain C < D < B < A < E is E, so E = 30 kilometres. Step 5: B travels exactly 15 kilometres. Since C and D are shorter, their distances must be less than 15 and distinct. Step 6: The question asks who can possibly travel 5 kilometres. The shortest distance must belong to C, so if any friend can travel 5 kilometres, it has to be C. Step 7: We can construct a consistent example: let C = 5, D = 10, B = 15, A = 20 and E = 30. All inequalities and conditions are satisfied, so this arrangement is valid and shows that C can indeed travel 5 kilometres. Verification / Alternative check: We should verify that none of the other friends can consistently be assigned 5 kilometres. D cannot travel 5 kilometres because D is second from the bottom, so C must be strictly shorter. B cannot travel 5 kilometres because B's distance is given as 15 kilometres. A and E are both greater than B, so they certainly cannot be at 5 kilometres. Therefore C is the only candidate who can logically and consistently travel 5 kilometres, which agrees with the model arrangement constructed earlier. Why Other Options Are Wrong: Option A, A, is impossible because A must travel more than 15 kilometres. Option C, D, is incorrect because D is second from the bottom and must have a distance strictly greater than C. Option D, E, is the one with the maximum distance, 30 kilometres, so E unquestionably cannot be at 5 kilometres. Option E, B, is ruled out by the explicit statement that B travels exactly 15 kilometres. Common Pitfalls: A frequent error is to misread "D travels more than only C" and assume it means D travels the most, when it actually states that only C is shorter, so D is second from the bottom. Another trap is to forget that all distances are distinct. Some learners also neglect the fixed distance of B and try to assign arbitrary small values to B, which contradicts the data. Drawing a simple ordered list, such as C < D < B < A < E, helps keep the relationships clear. Final Answer: The only friend who can consistently travel 5 kilometres without violating any condition is C.

Question 9

Facing the east, Rahul first turns towards his left and walks 10 metres. Then he again turns towards his left and walks another 10 metres. After that he turns towards his right and walks straight for 25 metres. In which direction is Rahul now standi…

Accepted Answer

Introduction / Context: Direction sense questions often involve a person starting in a known direction, then making several left and right turns, and finally asking about the direction of the final position relative to the starting point. In this problem Rahul starts facing east and makes a sequence of moves. We must track both his positions and facing directions carefully to conclude the final direction of his location from the starting point. Given Data / Assumptions: Rahul initially faces east at his starting point. He turns left and walks 10 metres. He then turns left again and walks another 10 metres. After that, he turns right and walks straight for 25 metres. All turns are right angles. We need the direction of Rahul's final position relative to the starting point, not the direction he is facing. Concept / Approach: A reliable technique is to place the starting point at the origin of a coordinate plane. We represent east as the positive x direction, west as negative x, north as positive y, and south as negative y. As Rahul turns left or right, his facing direction changes accordingly, and each movement updates his coordinates. After the sequence of movements, we compare his final coordinates with the origin to determine the direction: if x is positive and y is positive, the point lies in the north east quadrant, if x is negative and y is positive it lies in the north west, and so on. Step-by-Step Solution: Step 1: Suppose Rahul starts at point O with coordinates (0, 0), facing east. Step 2: From facing east, a left turn means he now faces north. Walking 10 metres north moves him to (0, 10). Step 3: From facing north, another left turn makes him face west. Walking 10 metres west moves him to (-10, 10). Step 4: From facing west, a right turn makes him face north again. He now walks 25 metres north, so his final position becomes (-10, 35). Step 5: His final coordinates are (-10, 35). The x coordinate is negative and the y coordinate is positive. Step 6: A point with negative x and positive y lies in the north west quadrant, so Rahul is to the north west of his starting point. Verification / Alternative check: We may visualise the path without coordinates. Starting from the origin facing east, the first left turn sends Rahul north for 10 metres. The second left turn sends him west for 10 metres, placing him diagonally north west of the origin. The final right turn sends him north again for an additional 25 metres, which means he moves even further north while remaining west of the starting point. Therefore he must be somewhere north west of the starting point, which confirms the coordinate calculation. Why Other Options Are Wrong: Option B, North-East, would require Rahul to be east of the origin, which conflicts with his 10 metre movement west in the middle of the path. Option C, South-West, would require a negative y coordinate; however he keeps moving north overall, ending with a large positive y value. Option D, South-East, also contradicts the overall movement, as he never ends up south of the starting point and does move west. Option E, West, would be correct only if his final vertical position aligned with the starting point, which is not the case because he is 35 metres north. Common Pitfalls: Many students confuse the direction of left and right turns when the facing direction is not the usual north. For example, from west a right turn leads to north, not south. Another common error is to focus on the last movement and forget earlier shifts that move the person west or north. Sketching the path or using a coordinate grid is an excellent way to avoid such mistakes and gives a clear visual representation of the final location. Final Answer: Rahul's final position is to the North-West of his starting point.

Question 10

Rita travels 35 kilometres from a certain point towards the south. She then turns left and travels 20 kilometres. Finally, she turns left again and travels another 35 kilometres. In which direction is Rita now located from her original starting poin…

Accepted Answer

Introduction / Context: Direction sense questions like this one require you to mentally or graphically track the path of a person as they move in steps with given distances and turns. The main target here is not the distance but the direction of the final position relative to the starting point. This problem uses two left turns after the initial southward movement, creating a rectangular path that is easy to follow if you draw a rough figure or use coordinate reasoning. Given Data / Assumptions: Rita starts at a fixed point, which we can treat as the origin. She travels 35 kilometres towards the south. She then turns left and travels 20 kilometres. Lastly, she turns left again and travels 35 kilometres. All turns are perpendicular (right angles). We must find the compass direction from the starting point to her final position. Concept / Approach: To solve, we can use a coordinate system where south corresponds to negative y, north to positive y, east to positive x and west to negative x. Each leg of Rita's journey updates her coordinates based on the current facing direction and the distance travelled. After calculating the final coordinates, we compare them to the origin. If the final x coordinate is positive and the y coordinate is zero, she is directly east of the starting point, and similar logic holds for other directions. Step-by-Step Solution: Step 1: Let Rita start at point O with coordinates (0, 0), facing south for the first movement. Step 2: She travels 35 kilometres south, so her position becomes (0, -35). Step 3: From facing south, a left turn makes her face east. She then travels 20 kilometres east to reach (20, -35). Step 4: From facing east, another left turn makes her face north. She travels 35 kilometres north to reach (20, 0). Step 5: The final coordinates are (20, 0). The x coordinate is positive and the y coordinate is zero. Step 6: A point with positive x and zero y lies directly to the east of the origin, so Rita is east of her starting point. Verification / Alternative check: We can also solve this geometrically without coordinates. The first and third movements are both 35 kilometres and are exactly opposite in direction (south then north), so they cancel each other vertically, bringing her back to the same north-south line as the starting point. During the middle movement of 20 kilometres east, she shifted horizontally from the original line and never returned in the opposite horizontal direction. Thus, at the end, she must be 20 kilometres directly east of the starting point, confirming the direction as east. Why Other Options Are Wrong: Option B, West, would require Rita to move in the opposite horizontal direction, which she never does. Option C, North, would require a final y coordinate greater than zero, but the north and south movements cancel each other out. Option D, South, would be correct only if there were more southward movement than northward, which is not the case here. Option E, North-East, is wrong because her vertical displacement is zero, so there is no northward component in her final position. Common Pitfalls: Students often forget that equal distances in opposite directions cancel out. Another common mistake is misidentifying left and right when the person is facing south or west, rather than north. Visualising or sketching the path step by step, or using arrows on paper, can greatly reduce confusion. Always check both horizontal and vertical components before deciding the final direction. Final Answer: Rita ends up directly to the East of her starting point.

Question 11

Abhinav starts his journey and travels 10 kilometres towards the north. Then he turns left and travels 6 kilometres. Next, he turns right and covers another 7 kilometres. Finally, he turns right once more and travels 6 kilometres. How far, in kilome…

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Introduction / Context: This problem is a direction sense and distance question combining several turns and segments of different lengths. Such questions can easily confuse learners if they only imagine the path mentally. The task is to find the straight line distance between Abhinav's starting point and his final position after moving north, then left, then right twice. The question checks spatial awareness and the ability to track movements using either a sketch or coordinate style reasoning. Given Data / Assumptions: Abhinav first travels 10 kilometres towards the north. He then turns left and travels 6 kilometres. After that he turns right and covers 7 kilometres. Finally he turns right again and travels another 6 kilometres. All turns are at right angles (90 degrees). We must find the straight line distance from the starting point to the final point. Concept / Approach: The most systematic method is to use a coordinate system. Choose the starting point as the origin (0, 0). Take north as positive y, south as negative y, east as positive x and west as negative x. At each step, update the coordinates based on the current facing direction and the distance travelled. Once we know the final coordinates, we can find the displacement using Pythagoras: distance = square root of (x^2 + y^2). Since all turns here are at right angles, the final displacement often turns out to be a simple integer value. Step-by-Step Solution: Step 1: Assume Abhinav starts at (0, 0), initially facing north. Step 2: He walks 10 kilometres north, so his position becomes (0, 10). Step 3: From facing north, a left turn leads to west. Walking 6 kilometres west, he reaches (-6, 10). Step 4: From facing west, a right turn leads back to north. Travelling 7 kilometres north, he reaches (-6, 17). Step 5: From facing north again, another right turn leads to east. Walking 6 kilometres east, he moves from (-6, 17) to (0, 17). Step 6: His final coordinates are therefore (0, 17). This means he is directly north of the starting point with no east or west displacement. Step 7: The straight line distance between (0, 0) and (0, 17) is simply 17 kilometres. Verification / Alternative check: We can confirm this result by tracking net vertical and horizontal movement. Horizontally, Abhinav first moves 6 kilometres west and later 6 kilometres east, which cancel out completely, leaving zero horizontal displacement. Vertically, he moves 10 kilometres north and an additional 7 kilometres north, with no southward movement, so his total vertical displacement is 17 kilometres north. Since only one component is non zero, the displacement distance is simply 17 kilometres, matching the coordinate approach. Why Other Options Are Wrong: Option A, 14 kilometres, may come from subtracting or incorrectly combining the vertical movements. Option B, 15 kilometres, and Option C, 16 kilometres, are typical distractors from mistaken Pythagoras applications or rough estimations. Option E, 13 kilometres, is another incorrect result that can arise from misreading the distances or mixing up left and right turns. Common Pitfalls: Common mistakes include confusing left and right when facing south or west, and failing to cancel out equal and opposite horizontal movements. Some students also attempt to add distances in different directions directly without using vector style reasoning. Drawing the path or maintaining a simple table of x and y coordinates at each step greatly reduces such errors and makes direction sense questions much easier to handle in timed exams. Final Answer: Abhinav is finally 17 kilometres away from his starting point, directly to the north, so the required distance is 17 kilometres.

Question 12

A woman in a shopping complex starts from a certain point and walks 250 metres towards the east. Then she turns towards the north and walks 100 metres. Next she turns towards the west and walks 120 metres. Finally she turns to her left and walks ano…

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Introduction / Context: This problem is another example of a direction sense and displacement question where a person follows a rectangular or nearly rectangular path with turns at right angles. We must determine the final position of the woman relative to where she started, focusing on net horizontal and vertical movement rather than the total distance actually walked. Such questions test both understanding of directions (north, south, east, west) and basic coordinate or geometric reasoning. Given Data / Assumptions: The woman starts at a certain point in a shopping complex. She walks 250 metres towards the east. She then turns north and walks 100 metres. Next she turns west and walks 120 metres. Finally she turns to her left and walks 100 metres. All turns are at right angles. We need her final position relative to the starting point in terms of both distance and direction. Concept / Approach: To solve, we use a coordinate grid. Let east be positive x, west be negative x, north be positive y and south be negative y. Each movement changes either the x coordinate or the y coordinate. After tracking all movements, we subtract the initial coordinates from the final coordinates to find net displacement. Because the final and initial y coordinates may cancel out, the net displacement often lies along one axis, making the direction easy to identify. Step-by-Step Solution: Step 1: Place the starting point at (0, 0). Step 2: The woman walks 250 metres east. This changes her x coordinate by +250, so her position becomes (250, 0). Step 3: She then turns north and walks 100 metres. This changes her y coordinate by +100, so her position becomes (250, 100). Step 4: Next she turns west and walks 120 metres, changing x by -120. Her new position is (130, 100). Step 5: Finally she turns left from facing west, which means she now faces south, and walks 100 metres. This changes y by -100, so her final position is (130, 0). Step 6: The final coordinates are (130, 0), which is 130 metres east of the origin and exactly on the same east-west axis. Verification / Alternative check: We can also reason without full coordinates by looking at horizontal and vertical movements separately. Horizontally, she first goes 250 metres east, then later 120 metres west. Net horizontal movement = 250 minus 120 = 130 metres east. Vertically, she goes 100 metres north and later 100 metres south, which cancel each other, leaving zero net vertical displacement. Therefore her final position must be 130 metres to the east of her starting point, confirming the coordinate method. Why Other Options Are Wrong: Option B, 130 metres West, reverses the actual horizontal direction. Option C, 370 metres East, is obtained by incorrectly adding 250 and 120 without considering that the 120 metres is towards the west. Option D, 370 metres West, is doubly incorrect because it both adds wrongly and uses the wrong direction. Option E, 250 metres North, ignores the cancellation of vertical movements and treats only the first vertical leg. Common Pitfalls: A typical error is to add all east and west movements without considering signs, which gives a value like 370 in the wrong direction. Another mistake is to forget that the final left turn from west leads to south, not north. Keeping a small rough sketch or table of net east-west and north-south movements is an efficient way to avoid confusion and quickly determine the correct displacement and direction. Final Answer: The woman is now located 130 metres East of her starting position.

Question 13

Rana walks 20 metres straight towards the north. Then he walks 20 metres towards his right. After that, at each subsequent left turn, he walks 5 metres, 25 metres and 25 metres respectively. How far is he now from his starting point, measured in a s…

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Introduction / Context: This problem combines several turns and different distances in a direction sense setting. The question tests the candidate's ability to correctly interpret right and left turns and then to derive the net displacement from the starting point. Because the path involves repeated turning and returning towards the general area of the starting point, it is especially important to keep track of both horizontal and vertical components of the movement. Given Data / Assumptions: Rana first walks 20 metres straight towards the north. Then he walks 20 metres towards his right, which is east when he is facing north. After that, he turns left and walks 5 metres. He turns left again and walks 25 metres. He turns left yet again and walks 25 metres. All turns are right angles. We need the straight line distance from the starting point to his final position. Concept / Approach: We will model the movement on a coordinate plane. Set the starting point at (0, 0). Let north be positive y, south negative y, east positive x and west negative x. As Rana walks and turns, we update his coordinates step by step. At the end, we use Pythagoras on the net horizontal and vertical changes to compute the shortest distance from the origin to the final point. In many such problems, because of symmetry and cancellation, the displacement becomes a simple integer. Step-by-Step Solution: Step 1: Start at (0, 0) facing north. Step 2: Rana walks 20 metres north to reach (0, 20). Step 3: Facing north, his right side is east. He walks 20 metres east, so his position becomes (20, 20). Step 4: Now he turns left from facing east, so he faces north and walks 5 metres, reaching (20, 25). Step 5: Turning left again from north means he now faces west. Walking 25 metres west takes him to (-5, 25). Step 6: Turning left again from west means he faces south. Walking 25 metres south brings him to (-5, 0). Step 7: The final coordinates are (-5, 0). Therefore he is 5 metres west of the starting point. Step 8: The straight line distance from (0, 0) to (-5, 0) is simply 5 metres. Verification / Alternative check: We can verify by net movement. Horizontally, Rana moves 20 metres east and later 25 metres west, giving a net 5 metres west. Vertically, he moves 20 metres north, then 5 metres north and finally 25 metres south. Net vertical movement = 20 + 5 minus 25 = 0 metres. Since the net vertical displacement is zero and the net horizontal displacement is 5 metres west, the shortest distance to the origin is 5 metres. This matches the coordinate based calculation exactly. Why Other Options Are Wrong: Option B, 20 metres, could arise if someone incorrectly uses only the first leg and ignores subsequent cancellations. Option C, 25 metres, might be chosen by those who mistake the largest single segment for the final displacement. Option D, 30 metres, may come from adding or subtracting distances without taking direction into account properly. Option E, 10 metres, is another random distractor with no basis in the net displacement calculation. Common Pitfalls: A major source of confusion is interpreting left and right as absolute instead of relative to the current facing direction. For instance, left from east is north, not west. Another frequent mistake is forgetting that multiple legs can cancel out each other in net displacement, leading to overestimation of distance. Always distinguish clearly between total distance walked and straight line displacement from the starting point. Final Answer: Rana is now 5 metres away from his starting point, so the required distance is 5 metres.

Question 14

In a particular faulty compass, the west direction in the real world is shown as south on the compass dial. According to this faulty compass, which indicated direction should a man follow if he actually wishes to move towards the true east direction?

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Introduction / Context: Reasoning questions involving faulty instruments, such as a misaligned compass, test a candidate's ability to reason about relative directions. Here the compass does not show the correct directions. We are told how it behaves for one known real direction, and we must deduce what reading on the faulty compass corresponds to another real direction. This is essentially a problem about rotation and mapping between actual directions and indicated directions on the misaligned dial. Given Data / Assumptions: In reality, there are four main directions: north, east, south and west. On the faulty compass, when a person actually faces west in the real world, the compass shows south. The misalignment is consistent for all directions (the compass card is rotated by a fixed angle). We have to find which direction the compass should indicate if the person wants to move towards the actual east direction. Concept / Approach: If a compass card is rotated, every real direction is shifted by the same amount on the dial. The statement that real west appears as south tells us that the dial has been rotated relative to the real world. We represent the real directions and the indicated directions as points on a circle, then determine the mapping. Once the mapping from real directions to compass readings is known, we apply the same shift to find which compass reading corresponds to real east. Step-by-Step Solution: Step 1: In the real world, the directions are arranged clockwise as North, East, South, West. Step 2: We are told that when a person stands facing real west, the compass indicates south. This means that the marking "south" on the compass dial physically points towards real west. Step 3: Therefore the whole dial appears to be rotated anticlockwise by 90 degrees relative to the real directions. Under this rotation, real west aligns with compass south. Step 4: Let us now compute how other real directions map. If the dial is rotated 90 degrees anticlockwise, then real north aligns with compass west, real east aligns with compass north, real south aligns with compass east and real west aligns with compass south. Step 5: The question asks: if the man wishes to move towards the real east direction, which compass indication should he follow? Step 6: From the mapping above, real east corresponds to compass north. So he should move in the direction that the faulty compass labels as north. Verification / Alternative check: We can verify by drawing a simple circle with the real directions marked, then physically rotating the compass labels anticlockwise by one quadrant. Place N, E, S, W on a circle. Now rotate the dial anticlockwise so that the label S moves to the position of W. After rotation, label N shifts to the position of E, label E to the position of S and label W to the position of N. Therefore when the compass shows north, the person is actually facing east in the real world. This matches our earlier reasoning. Why Other Options Are Wrong: Option B, South, corresponds to real west, which is given in the question as the faulty indication. Option C, East, would correspond to real south under the anticlockwise rotation and so is incorrect for reaching real east. Option D, West, matches real north under the same mapping and therefore does not satisfy the requirement. Option E, North-East, is not involved in the simple quarter turn rotation described and is not supported by the mapping information. Common Pitfalls: Many learners mistakenly assume that the compass is rotated clockwise or that each direction simply shifts by arbitrary amounts. It is crucial to remember that all directions move together as a rigid rotation. Forgetting to apply the same shift to each direction leads to incorrect answers. Drawing a diagram with arrows for real and indicated directions is often the quickest and most reliable method for such problems. Final Answer: To move towards the real east direction, the man should follow the direction that the faulty compass shows as North.

Question 15

Neeraj is initially facing north. He first turns 45 degrees to his right and walks 25 metres. Then he turns so that he faces the south east direction and walks another 25 metres. From there he walks 25 metres towards the east. In which direction is …

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Introduction / Context: This problem is a slightly more advanced direction sense question because it uses diagonal movements such as 45 degree turns and movement along the south east direction. Instead of only orthogonal north, south, east and west legs, we have north east and south east components. The objective is to track Neeraj's net displacement and determine the compass direction of his final position relative to where he started. Given Data / Assumptions: Neeraj starts facing north. He turns 45 degrees to his right, which makes him face north east, and then walks 25 metres. Next he turns so that he faces south east and walks another 25 metres. Finally, from that point, he walks 25 metres towards the east. We assume ideal directions: north east means 45 degrees between north and east, and south east means 45 degrees between south and east. We must find the direction of his final position from his original starting point. Concept / Approach: Because diagonal movements are involved, the most systematic approach is to break each displacement into horizontal (east west) and vertical (north south) components. For movements of 25 metres at 45 degrees, the horizontal and vertical components are equal and can be expressed as 25 divided by square root of 2 in magnitude, one positive and one negative depending on the quadrant. After summing the components of all three legs, we can determine whether Neeraj ends up to the east, west, north or south of the starting point and in which quadrant, if any. Step-by-Step Solution: Step 1: Choose a coordinate system with the starting point at (0, 0). Let east be positive x and north be positive y. Step 2: After turning 45 degrees right from north, Neeraj faces north east. A 25 metre move in this direction has components: x = 25 divided by square root of 2, y = 25 divided by square root of 2. So after the first leg, his position is approximately (17.68, 17.68). Step 3: He then turns to face south east. This direction has x positive and y negative. A 25 metre move gives components x = 25 divided by square root of 2, y = minus 25 divided by square root of 2. Adding these to the previous coordinates yields (35.36, 0). Step 4: From this point he walks 25 metres directly east. That changes only the x coordinate. His final position becomes (35.36 + 25, 0) which is approximately (60.36, 0). Step 5: The final y coordinate is zero and the final x coordinate is positive. Thus Neeraj is directly to the east of his starting point, with no north or south component. Verification / Alternative check: We may also reason qualitatively. The first and second legs are symmetric diagonal moves: one goes north east and the other south east, each 25 metres. Their vertical components cancel because one is northward and the other is equally southward. However, their horizontal components both point eastward and therefore add up. After these two moves, Neeraj is some distance directly to the east of the starting point. The last leg of 25 metres east simply increases this eastward displacement. Therefore he must end up exactly east of his starting position, which matches the coordinate based conclusion. Why Other Options Are Wrong: Option A, North, would require a net positive y component, which we do not have because the north and south components cancel. Option B, West, would correspond to a negative x component, but all movements have eastward horizontal components. Option D, South, would require a net negative y component, which again is not present after cancellation. Option E, South-East, would require both positive x and negative y displacement; however the net vertical displacement is zero. Common Pitfalls: The main difficulty in such problems is correctly handling diagonal movements. Students often forget that north east and south east have equal magnitude components in perpendicular directions, and they mistakenly add or subtract distances without decomposition. Another common mistake is to misinterpret the second turn and add both vertical components instead of cancelling them. Using simple vector components or a rough geometric diagram prevents these errors and makes the pattern of cancellation clear. Final Answer: Neeraj's final position lies directly to the East of his original starting point.

Question 16

A man moves 24 metres in the south direction from his starting point. He then turns 90 degrees anticlockwise and moves another 7 metres. After this he takes a right turn and moves 3 metres and then moves 3 metres in the north direction. What is the …

Accepted Answer

Introduction / Context: Here we have a direction sense question involving southward movement, an anticlockwise turn, and a couple of short segments. We are asked for the straight line distance between the starting and final positions, which is the net displacement. These questions assess whether a candidate can correctly interpret anticlockwise and clockwise turns relative to the current direction and then combine movements using basic geometry or coordinate reasoning. Given Data / Assumptions: The man starts at a fixed point. He walks 24 metres towards the south. He then turns 90 degrees anticlockwise and moves 7 metres. Next he turns right and moves 3 metres. Finally he moves 3 metres towards the north. All turns are at right angles and distances are exact. We have to find the straight line distance between initial and final positions. Concept / Approach: We use a coordinate system: let the starting point be at (0, 0), with east as positive x and north as positive y. Moving south reduces y, moving east increases x, and so on. An anticlockwise turn means turning left when viewed from above. After updating the coordinates with each movement, we compute the displacement as the square root of (x^2 + y^2). Because the path involves a right-angle triangle pattern, the final distance often comes out as a simple Pythagorean number. Step-by-Step Solution: Step 1: Start at (0, 0). The man moves 24 metres south, so his new position is (0, -24). Step 2: From facing south, a 90 degree anticlockwise turn makes him face east. Walking 7 metres east moves him to (7, -24). Step 3: From facing east, a right turn makes him face south. Moving 3 metres south puts him at (7, -27). Step 4: He then moves 3 metres north, which changes y by +3, so his final position is (7, -24). Step 5: The coordinates of the starting point are (0, 0) and those of the final point are (7, -24). Step 6: The straight line distance between these points is square root of (7^2 + 24^2) = square root of (49 + 576) = square root of 625 = 25 metres. Verification / Alternative check: We can check net horizontal and vertical movement separately. Horizontally, the man only moves 7 metres east; no later movement changes his x coordinate, so net x displacement is 7 metres. Vertically, he walks 24 metres south and later 3 metres south, then 3 metres north, for a net vertical movement of 24 metres south. Therefore the displacement forms a right triangle with legs 7 and 24. The well known Pythagorean triple 7, 24, 25 confirms that the hypotenuse, which is the displacement, equals 25 metres. Why Other Options Are Wrong: Option B, 30 metres, would require larger legs or incorrect addition of distances without using Pythagoras. Option C, 27 metres, can come from wrongly adding 24 and 3 instead of working with the squared components. Option D, 35 metres, is another arbitrary value that does not match the geometry of this triangle. Option E, 20 metres, ignores the full southward displacement and is not supported by the calculations. Common Pitfalls: One common mistake is misinterpreting anticlockwise from south as west instead of east. Another error is to simply add or subtract all distances ignoring direction and the Pythagoras theorem. Students should practice identifying classical right triangles like 3, 4, 5 or 7, 24, 25, which appear frequently in aptitude questions, to quickly verify their answers under exam pressure. Final Answer: The man ends up 25 metres away from his starting point, so the required distance is 25 metres.

Question 17

Arjun is facing east. He first walks 10 metres in the east direction. Then he turns left and walks another 10 metres. Next, he turns right and walks 25 metres. From there he walks 10 metres towards the south. Finally, he walks 50 metres towards his …

Accepted Answer

Introduction / Context: This direction sense question combines several orthogonal movements (east, north, south) with left and right turns. We are required to find the straight line distance between Arjun's starting point and his final position, after he traverses a somewhat rectangular path and then makes a long final move. These problems test a candidate's ability to track position step by step and then use basic geometry to find the net displacement. Given Data / Assumptions: Arjun initially faces east. He walks 10 metres east. He then turns left (towards north) and walks 10 metres. Next he turns right (towards east) and walks 25 metres. From there he walks 10 metres towards the south. Finally he walks 50 metres towards his left, relative to his last facing direction. All turns are right angle turns. We must calculate the straight line distance from his original position to his final position. Concept / Approach: We will model the situation on a coordinate plane. Treat Arjun's starting point as (0, 0). East is positive x, west negative x, north positive y, south negative y. Each movement changes either x or y while the other coordinate remains constant. After tracking all five legs of the journey, we compute the net horizontal and vertical displacement, then apply Pythagoras: distance = square root of (x^2 + y^2). Step-by-Step Solution: Step 1: Start at (0, 0), facing east. After walking 10 metres east, Arjun is at (10, 0). Step 2: From facing east, a left turn makes him face north. Walking 10 metres north, he reaches (10, 10). Step 3: From facing north, a right turn takes him back to facing east. Walking 25 metres east, he moves to (35, 10). Step 4: He then walks 10 metres south, so his y coordinate decreases by 10, giving a new position (35, 0). Step 5: At this point he is facing south (because his last movement was south). From facing south, his left side is east. Walking 50 metres towards his left means 50 metres east, so he moves to (85, 0). Step 6: The final coordinates are (85, 0). This means he is 85 metres east of the starting point with no north-south displacement. Step 7: The straight line distance from (0, 0) to (85, 0) is simply 85 metres. Verification / Alternative check: We can compute net horizontal and vertical components directly. Horizontally, Arjun moves 10 metres east in the first leg, 25 metres east in the third leg, and 50 metres east in the final leg, for a total of 10 + 25 + 50 = 85 metres east. There is no westward motion. Vertically, he moves 10 metres north and then 10 metres south, which cancel each other out, leaving zero net vertical displacement. Hence the displacement vector is purely horizontal with magnitude 85 metres, confirming our coordinate reasoning. Why Other Options Are Wrong: Option B, 80 metres, may come from forgetting one of the eastward segments. Option C, 75 metres, could arise from incorrectly adding 10, 25 and 40 instead of 50 for the last leg. Option D, 90 metres, results from naive addition of an extra 5 metres somewhere without justification. Option E, 70 metres, is a random underestimation not supported by the exact calculations. Common Pitfalls: Students often misinterpret which direction is left when the person is facing south or west. Another common issue is mixing up total distance walked with net displacement. Total distance is the sum of all segments, but displacement considers only the straight line between start and finish. Drawing a quick sketch with arrows corresponding to each step usually clarifies the path and prevents these errors. Final Answer: Arjun is now 85 metres away from his starting point, directly to the east, so the required distance is 85 metres.

Question 18

It is exactly 10:30 by the clock. If, at this moment, the minute hand is pointing towards the south direction, then in which compass direction will the hour hand be pointing?

Accepted Answer

Introduction / Context: Clock and direction problems connect the positions of clock hands with compass directions. At certain times the hour and minute hands form specific angles relative to the 12 o clock position. If one hand is aligned with a known cardinal direction, we can deduce the direction of the other hand. In this question we know it is 10:30 and the minute hand points south, and we must determine the direction of the hour hand. Given Data / Assumptions: The time is exactly 10:30. The minute hand is pointing towards the south direction. We assume a standard analog clock where 12 is at the top, 3 at the right, 6 at the bottom and 9 at the left. We must find the compass direction (such as north west or south east) of the hour hand. Concept / Approach: At 10:30, the minute hand is at the 6 on the clock, which is directly opposite the 12. The hour hand is between 10 and 11, slightly closer to 11. On a standard clock that is not rotated, 12 corresponds to north, 3 to east, 6 to south and 9 to west. Because we are told specifically that the minute hand points south at 10:30, the clock's normal orientation is already aligned with compass directions. Hence we identify the geometric position of the hour hand on the dial and match that with the appropriate compass direction. Step-by-Step Solution: Step 1: At 10:30, the minute hand points at the 6. On a standard clock face, 6 is directly downward from the centre, opposite 12. Step 2: The problem states that at this time, the minute hand points towards the south. This matches the usual convention where the downward direction corresponds to south, so no rotation is required. Step 3: Now we analyse the hour hand. At exactly 10:00 the hour hand points at the 10, which is between 9 (west) and 11 (north west region). Step 4: Between 10:00 and 11:00, the hour hand slowly moves from the 10 mark towards the 11 mark. At 10:30 it is halfway between the 10 and 11 positions. Step 5: The 9 mark is directly west, the 12 mark is directly north. The 10 and 11 marks lie between these two, with both leaning towards the north west quadrant. Step 6: Therefore, halfway between 10 and 11 is still firmly in the north west region of the clock face. Step 7: Since the clock is aligned such that 12 is north and 9 is west, the intermediate position of the hour hand at 10:30 corresponds to a north west direction. Verification / Alternative check: An alternative is to think in terms of angles. The full circle is 360 degrees, and there are 12 hours, so each hour marking is 30 degrees apart. At 10:30, the hour hand is at 10.5 hours from the top. Measured clockwise from 12, the angle is 10.5 multiplied by 30 degrees, which equals 315 degrees. On a compass, 0 degrees corresponds to north and 90 degrees to east. A bearing of 315 degrees lies between 270 degrees (west) and 360 degrees (north), nearer to north and west, which is precisely the north west direction. Why Other Options Are Wrong: Option A, South-West, points downwards and to the left, inconsistent with the upper left position of the hour hand at 10:30. Option C, North-East, describes an upwards and rightwards direction, opposite to the hour hand's location on the left side of the clock. Option D, South-East, lies in the bottom right quadrant and is incompatible with the hour hand being above the centre between 10 and 11. Option E, West, would align with the 9 o clock position, but at 10:30 the hour hand is clearly above and to the right of west. Common Pitfalls: Students sometimes forget that the hour hand moves continuously and is not fixed exactly on the hour marks at half past times. Others may incorrectly rotate the clock instead of matching it with the given minute hand direction. Always check whether the description of the minute hand matches the standard orientation. If it does, no extra rotation is needed, simplifying the reasoning considerably. Final Answer: At 10:30, with the minute hand pointing south, the hour hand points towards the North-West direction.

Question 19

Meet starts cycling early in the morning while facing the Sun, so he is initially facing east. After some time, he takes a 45 degree turn to his left. Then he again turns 80 degrees towards his left. In which direction is he now with respect to his …

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Introduction / Context: This question combines knowledge of the Sun's direction in the morning with angular turns measured in degrees. It tests whether candidates can track cumulative rotations from an initial facing direction. Meet starts by facing east, then makes two left turns of 45 degrees and 80 degrees respectively. The challenge is to identify the final compass direction he faces after adding these rotations. Given Data / Assumptions: Early in the morning, the Sun appears in the east, so Meet initially faces east. He first turns 45 degrees to his left from the east direction. He then makes another turn of 80 degrees to his left. We assume all degree measures are exact and measured in the usual geometric sense. We need the final compass direction that he faces after these two left turns. Concept / Approach: Facing east corresponds to a direction 90 degrees clockwise from north if we use the usual bearing convention, but for this problem it is simpler to think in terms of the four quadrants. East is to the right, north is up, west is left and south is down. A left turn from east takes us towards north. By adding the angles of the two left turns, we find the total anticlockwise rotation from east and then determine which quadrant that final direction falls into. Step-by-Step Solution: Step 1: Meet is initially facing east. Step 2: A left turn is an anticlockwise rotation. From east, turning 90 degrees left would make him face north. However, he turns only 45 degrees left, so he faces exactly halfway between east and north, which is the north east direction. Step 3: From the north east direction, he turns another 80 degrees to his left. Step 4: The total leftward rotation from the original east direction is 45 degrees plus 80 degrees, which equals 125 degrees. Step 5: Now map this total rotation. From east, rotating 90 degrees left brings him to north. An additional 35 degrees left (since 125 minus 90 equals 35) moves him beyond north towards the west. Step 6: Therefore, after a total rotation of 125 degrees, he is in the quadrant between north and west, closer to west than north but still above the horizontal axis, which is the north west direction. Verification / Alternative check: An angular bearing view can also be used. Let east be 0 degrees, north be 90 degrees, west be 180 degrees and south be 270 degrees. A left turn from east increases the angle. After 125 degrees anticlockwise rotation from east, the bearing is 125 degrees from east, which corresponds to 90 plus 35 degrees from north, hence lying between north (90) and west (180). Since 125 degrees is less than 180 degrees, the direction is in the north west quadrant, which confirms the earlier reasoning. Why Other Options Are Wrong: Option A, South-East, would be in the opposite quadrant, requiring a rotation towards the south rather than north. Option B, South-West, is too far anticlockwise, corresponding to rotations greater than 180 degrees. Option D, North-East, would be correct if the second left turn were small or zero; however the additional 80 degrees pushes him beyond north. Option E, West, would require a total rotation of exactly 180 degrees from east, not the given 125 degrees. Common Pitfalls: Many students treat the two left turns as independent and forget to combine them, or they misinterpret 45 degrees plus 80 degrees as a full right angle. Others incorrectly believe that any series of left turns from east will always lead exactly to north or west. Accurately adding the degree measures for rotations and then mapping them on a simple compass-like circle is a reliable way to avoid such mistakes. Final Answer: After turning 45 degrees and then 80 degrees to his left from the east, Meet is facing towards the North-West direction.

Question 20

Ram walks 20 metres towards the north from his starting point. Then he turns towards the east and walks another 5 metres. After that, he turns towards his right and covers 20 metres. How far is he from the starting point now, measured in a straight …

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Introduction / Context: This question is another example of direction and distance reasoning, where the path forms an almost rectangular pattern. The candidate must track Ram's steps north, then east, then a final direction determined by a right turn, and finally compute the net displacement from the starting point. It checks whether the student understands relative turns and can translate the movement into simple geometry to find the shortest distance between the initial and final points. Given Data / Assumptions: Ram starts from a fixed point. He goes 20 metres towards the north. He then turns towards the east and walks 5 metres. After that he turns towards his right and covers 20 metres. All turns are at right angles. We must find the straight line distance from his starting point to his final position. Concept / Approach: As usual, we set up a coordinate system. Take Ram's starting point as (0, 0), with north as positive y and east as positive x. Each leg of the journey moves him along one coordinate axis. A right turn changes the facing direction by 90 degrees clockwise. After all movements, we find the difference between final and initial coordinates and then use Pythagoras: distance = square root of (x^2 + y^2). Because the path contains symmetric vertical movements, displacement may be small compared to total distance walked. Step-by-Step Solution: Step 1: Start at (0, 0). Walking 20 metres north moves Ram to (0, 20). Step 2: From facing north, turning towards the east means he now faces east. Walking 5 metres east moves him to (5, 20). Step 3: From facing east, a right turn is a turn towards the south. Walking 20 metres south reduces the y coordinate by 20, bringing him to (5, 0). Step 4: So the final position is (5, 0), that is 5 metres east of the starting point with no net north-south displacement. Step 5: The straight line distance between (0, 0) and (5, 0) is simply 5 metres. Verification / Alternative check: Without coordinates, we may reason in terms of net vertical and horizontal movement. Vertically, Ram walks 20 metres north and later 20 metres south. These movements cancel each other perfectly, leaving zero net vertical displacement. Horizontally, he only walks 5 metres east and no westward segments. Hence the net displacement is a simple 5 metres east. This matches the coordinate based method exactly and confirms that the answer is 5 metres. Why Other Options Are Wrong: Option A, 3 metres, and Option B, 4 metres, represent smaller lengths with no basis in the geometry of this path. Option D, 6 metres, may arise from adding an extra metre due to an arithmetic mistake. Option E, 10 metres, might be chosen by those who confuse total distance and displacement or roughly estimate the diagonal without correct calculation. Common Pitfalls: Some students forget that equal distances north and south cancel each other, leading them to treat the 20 metre legs as contributing to net displacement. Others misinterpret the right turn from east as west instead of south. Drawing a quick figure or diagram with arrows for each movement is an efficient way to avoid these confusions. Always distinguish carefully between total path length and the straight line distance from start to finish. Final Answer: Ram is now 5 metres away from his starting point, so the required distance is 5 metres.

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