Question 1

A person starts walking towards the west and covers a distance of 15 metres. He then turns right and walks 10 metres. Again he turns right and walks 5 metres, and in the end he turns left and walks 15 metres. In which direction is this person finall…

Accepted Answer

Introduction / Context:
Instead of asking for displacement, this direction sense question asks for the final facing direction of a person after a series of right and left turns. Such questions test whether candidates can track relative turns correctly from any current orientation, not just from north. The actual distances travelled are irrelevant for the final facing direction, but they often appear to distract the learner.

Given Data / Assumptions:

The person starts by walking 15 metres towards the west.
He then turns right and walks 10 metres.
Next he turns right again and walks 5 metres.
Finally he turns left and walks 15 metres.
Every turn is a 90 degree right angle.
We must find the direction he is facing after the last movement, not his position.

Concept / Approach:
The key is to trace the sequence of directions in which the person is facing. Distances do not influence the final facing direction, only the turns do. Whenever the person turns right, we rotate his facing direction 90 degrees clockwise; for a left turn, we rotate 90 degrees anticlockwise. By following this sequence from the initial facing direction of west, we determine his final orientation after all turns.

Step-by-Step Solution:
Step 1: Initially, the person is walking towards the west, so he is facing west.
Step 2: He then turns right. From west, a right turn means facing north.
Step 3: Walking 10 metres in this direction does not change his facing direction; he continues to face north.
Step 4: Again he turns right. From facing north, a right turn leads to facing east.
Step 5: He walks 5 metres while facing east and remains facing east at the end of this segment.
Step 6: Finally he turns left. From facing east, a left turn leads to facing north.
Step 7: He walks 15 metres while facing north, so his final facing direction is north.

Verification / Alternative check:
We can represent the four cardinal directions in order clockwise as North, East, South, West. Each right turn moves one step forward in this list, and each left turn moves one step backward. Starting from West, one right turn takes us to North, another right turn to East, and one left turn brings us back to North. This confirms that, regardless of the distances walked, the final facing direction must be north.

Why Other Options Are Wrong:

Option B, South, would require either an odd number of turns leading through east to south or a different starting direction; the given sequence does not support this.
Option C, East, would be correct if the last turn had been to the right instead of left.
Option D, West, would require a net rotation of zero or a full multiple of 360 degrees, which is not the case here.
Option E, North-East, involves a diagonal direction not produced by 90 degree right and left turns in this sequence.

Common Pitfalls:
A typical mistake is to pay unnecessary attention to distances, which may distract from tracking orientation. Another frequent error arises from misinterpreting left and right when facing directions other than north. A simple mental or physical model of the four main directions arranged in order helps to apply rotations correctly and quickly determine final orientation.

Final Answer:
After all the turns, the person is finally facing towards the North direction.

Question 2

Two trucks, A and B, start from the same warehouse. Truck A goes 6 kilometres towards the north and then turns to its right and goes 4 kilometres. Meanwhile, truck B goes 9 kilometres towards the east, then turns towards the north and goes 6 kilomet…

Accepted Answer

Introduction / Context:
This is a relative position problem with two moving objects, trucks A and B, starting from the same warehouse but following different routes. The goal is to track the final coordinates of each truck and then compute the displacement of truck B with respect to truck A. Problems of this type test a student's ability to apply coordinate reasoning to multiple moving entities at the same time.

Given Data / Assumptions:

Both trucks start from the same warehouse, treated as the origin.
Truck A goes 6 kilometres north, then turns right and goes 4 kilometres.
Truck B goes 9 kilometres east, then 6 kilometres north, and then 4 kilometres to its right from that direction.
All turns are right angle turns.
We must find the position of truck B relative to truck A, that is, where B is located with respect to A.

Concept / Approach:
We use the coordinate system where east is positive x, north is positive y, west negative x and south negative y. We first find the final coordinates of truck A, then the final coordinates of truck B. To get the position of B with respect to A, we subtract A's coordinates from B's coordinates. The direction and distance of this difference vector tell us the required relative location.

Step-by-Step Solution:
Step 1: Place the warehouse at (0, 0).
Step 2: For truck A, going 6 kilometres north moves it to (0, 6).
Step 3: From facing north, a right turn leads east. Moving 4 kilometres east takes truck A to (4, 6). This is the final position of truck A.
Step 4: For truck B, going 9 kilometres east moves it to (9, 0).
Step 5: From facing east, turning towards the north and going 6 kilometres takes truck B to (9, 6).
Step 6: From facing north, a right turn leads east. Moving 4 kilometres east moves truck B to (13, 6). This is the final position of truck B.
Step 7: Now we find the displacement of B with respect to A by subtracting A's coordinates from B's coordinates: (13, 6) minus (4, 6) equals (9, 0).
Step 8: A difference of (9, 0) means truck B is 9 kilometres east of truck A.

Verification / Alternative check:
We can think qualitatively. Both trucks eventually reach the same northward level (y coordinate 6 kilometres north of the warehouse), because truck A goes up 6 kilometres and truck B also goes up 6 kilometres after its eastward movement. Horizontally, truck A ends 4 kilometres east of the warehouse, while truck B ends 13 kilometres east (9 plus another 4). Differences in eastward distances are therefore 13 minus 4 = 9 kilometres. Since there is no difference in their north-south positions, B must be exactly 9 kilometres east of A.

Why Other Options Are Wrong:

Option A, 17 kilometres East, incorrectly adds some distances without tracking coordinates precisely.
Option B, 9 kilometres West, has the correct magnitude but the wrong direction, reversing east and west.
Option C, 17 kilometres West, is incorrect both in magnitude and direction.
Option E, 5 kilometres East, is an underestimation that does not match the computed coordinate difference.

Common Pitfalls:
A common mistake is to subtract the wrong coordinates or to neglect that both trucks end up at the same vertical level. Some learners also confuse the relative phrase "with respect to truck A" and instead compute the position of A from B. Always verify the relative direction by picturing A at its final point and visualising how far and in which direction one must travel to reach B.

Final Answer:
Truck B is located 9 kilometres East of truck A.

Question 3

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

Accepted Answer

Introduction / Context:
This question features several points placed relative to each other in a plane, described using directions and distances. The challenge is to compute the coordinates of each point step by step, and then determine the displacement from point A to point G. It is a typical reasoning problem that blends spatial visualisation with basic coordinate geometry and is often used to test careful reading and systematic tracking of multiple relationships.

Given Data / Assumptions:

Point A is 8 metres west of point B.
Point C is 4 metres south of point B.
Point D is 4 metres east of point C.
Point F is 6 metres north of point D.
Point E is 8 metres west of point F.
Point G is 2 metres south of point E.
All directions are exact, and movements are along cardinal directions.
We need the distance and direction from point A to point G.

Concept / Approach:
We will choose point B as the origin of a coordinate system for convenience. Then we can represent each point with coordinates based on its relative position to B or another known point. East is positive x, west negative x, north positive y and south negative y. After we compute coordinates for A through G, we find the displacement vector from A to G by subtracting coordinates. The magnitude and sign of this vector reveal the required distance and direction.

Step-by-Step Solution:
Step 1: Let point B be at (0, 0).
Step 2: Point A is 8 metres to the west of B, so A is at (-8, 0).
Step 3: Point C is 4 metres south of B, so C is at (0, -4).
Step 4: Point D is 4 metres east of C. From (0, -4), moving 4 metres east gives D at (4, -4).
Step 5: Point F is 6 metres north of D, so from (4, -4) we add 6 in the y direction to get F at (4, 2).
Step 6: Point E is 8 metres west of F. From (4, 2), moving 8 metres west gives E at (-4, 2).
Step 7: Point G is 2 metres south of E. From (-4, 2), moving 2 metres south gives G at (-4, 0).
Step 8: Now we have A at (-8, 0) and G at (-4, 0). The displacement from A to G is found by subtracting coordinates: (-4, 0) minus (-8, 0) equals (4, 0).
Step 9: A displacement of (4, 0) means G is 4 metres to the east of A.

Verification / Alternative check:
We can also reason qualitatively. Notice that A and B lie on a horizontal line with A 8 metres west of B. The construction from B down to C, across to D, up to F, and then west to E and south to G eventually brings G back to the same vertical level as A and B because G has y coordinate 0. Observing that E is 8 metres west of F, and F is 4 metres east of C, we find E is 4 metres west of C. Then G is 2 metres south of E, but this only changes the vertical coordinate, not the relative position to A along the horizontal axis at the y equals 0 line. Hence G must lie 4 metres east of A, confirming our calculation.

Why Other Options Are Wrong:

Option B, 8 metres to the West, reverses both magnitude and direction; G is not further west than A.
Option C, 4 metres to the West, has the correct magnitude but wrong direction.
Option D, 8 metres to the East, doubles the correct magnitude.
Option E, 2 metres to the South, describes a vertical displacement from E instead of from A and so is not relevant to the question asked.

Common Pitfalls:
With many points, it is easy to lose track of the intermediate coordinates or mix up east and west. Students may also forget that we are asked about G relative to A, not relative to B. Writing down coordinates step by step or drawing a simple grid significantly reduces the cognitive load and prevents errors in such multi stage reasoning problems.

Final Answer:
Point G is located 4 metres to the East of point A.

Question 4

Two village women are returning home starting from the same point. The first woman walks 1 kilometre towards the south and then turns to her right and walks 6 kilometres to reach her house. In the meantime, the second woman walks 5 kilometres toward…

Accepted Answer

Introduction / Context:
This is a relative position problem in which two people start from the same point but follow different paths to reach their respective homes. We are asked to find where the second woman's house lies relative to the first woman's house. Such questions test whether the candidate can compute the final coordinates of each person and then determine the relative displacement between those two final points rather than between any of them and the origin.

Given Data / Assumptions:

Both women start from the same common point.
The first woman walks 1 kilometre south, then turns right and walks 6 kilometres to reach her house.
The second woman walks 5 kilometres west, then 4 kilometres north, and finally 1 kilometre to her left from that direction to reach her house.
All directions are along cardinal directions and turns are right angles.
We must find the location of the second woman's house relative to the first woman's house.

Concept / Approach:
We adopt coordinate geometry. Let the starting point be (0, 0). Take east as positive x, north as positive y, west as negative x and south as negative y. We first compute the coordinates of the first woman's house and then of the second woman's house. The vector from the first house to the second house is found by subtracting their coordinates, which then gives the required distance and direction.

Step-by-Step Solution:
Step 1: The starting point is (0, 0).
Step 2: For the first woman: walking 1 kilometre south moves her to (0, -1).
Step 3: From facing south, a right turn means facing west. Walking 6 kilometres west moves her to (-6, -1). This is the position of the first house.
Step 4: For the second woman: walking 5 kilometres west from (0, 0) moves her to (-5, 0).
Step 5: From facing west, turning towards the north means she now faces north. Walking 4 kilometres north moves her to (-5, 4).
Step 6: From facing north, a left turn means facing west. Walking 1 kilometre west moves her to (-6, 4). This is the position of the second house.
Step 7: The first house is at (-6, -1) and the second house is at (-6, 4).
Step 8: To find the second house relative to the first, we subtract: (-6, 4) minus (-6, -1) equals (0, 5).
Step 9: A difference of (0, 5) means the second house lies 5 kilometres north of the first house.

Verification / Alternative check:
We can ignore the origin and make a simpler statement: both houses are on the same vertical line x equals minus 6, because each last horizontal move takes them to that line. The first woman's last position has y coordinate minus 1, while the second woman's final y coordinate is plus 4. The second house is therefore directly north of the first by 4 minus minus 1 equals 5 kilometres. This matches the coordinate subtraction result exactly.

Why Other Options Are Wrong:

Option B, 3 kilometres North, underestimates the difference of 5 kilometres between the y coordinates of the two houses.
Option C, 5 kilometres South, reverses the direction; the second house is north, not south, of the first house.
Option D, 3 kilometres South, is wrong in both magnitude and direction.
Option E, 1 kilometre East, suggests a horizontal separation that does not exist since both houses share the same x coordinate.

Common Pitfalls:
Students sometimes compute each house's position relative to the starting point correctly but then forget that the question asks for relative position between the houses, not between a house and the origin. Another common error is misinterpreting "left" from the north as east instead of west. Using coordinates and carefully subtracting them for relative positions is a robust strategy to avoid confusion.

Final Answer:
The second woman's house is located 5 kilometres North of the first woman's house.

Question 5

Amit is facing north. He turns 90 degrees to his right and walks for 50 metres. Then he turns towards the south and walks 50 metres. Next he turns right again and walks another 50 metres and, from there, he walks 50 metres towards the north. In whic…

Accepted Answer

Introduction / Context:
This direction sense question describes Amit walking in a path that resembles a square or rectangle and then asks about his final location relative to the starting point. Although there are multiple turns and equal distances, the overall effect may cancel, bringing him back to where he started. The problem tests whether candidates can recognise and confirm such symmetric paths using systematic reasoning.

Given Data / Assumptions:

Amit is initially facing north.
He turns 90 degrees to his right and walks 50 metres.
He then turns towards the south and walks 50 metres.
Next he turns right again and walks another 50 metres.
From there he walks 50 metres towards the north.
All movements are along cardinal directions and turns are perpendicular.
We must determine where he is relative to the original starting point.

Concept / Approach:
We will map Amit's path on a coordinate plane. Place his starting point at (0, 0), with north as positive y and east as positive x. Each movement updates either the x or y coordinate. Because the distances are equal (all 50 metres) and movements form a loop, we suspect he may return to the origin, but we will confirm this by explicit calculation. This type of reasoning ensures we do not rely on visual guesses alone.

Step-by-Step Solution:
Step 1: Begin at (0, 0), facing north.
Step 2: Turning 90 degrees right from north makes Amit face east. Walking 50 metres east moves him to (50, 0).
Step 3: From facing east, turning towards the south means facing south. Walking 50 metres south moves him to (50, -50).
Step 4: From facing south, a right turn makes him face west. Walking 50 metres west moves him from (50, -50) back to (0, -50).
Step 5: Finally, from facing west, he walks 50 metres north. This increases the y coordinate by 50, moving him from (0, -50) to (0, 0).
Step 6: The final coordinates are (0, 0), which are exactly the same as the starting coordinates.
Step 7: Therefore, Amit returns to his original position.

Verification / Alternative check:
We can see that Amit essentially walks around the four sides of a square of side 50 metres. He starts at one corner, goes east 50 metres, then south 50 metres, then west 50 metres, and finally north 50 metres. Such a closed loop always brings him back to the starting corner. As long as each side is equal and the sequence of turns is consistent, the path is a complete circuit, which confirms that his final position coincides with the initial position.

Why Other Options Are Wrong:

Option A, South-West, would imply a net negative x and y displacement, which is not the case once we consider the full loop.
Option C, North-East, would require positive x and y coordinates at the end, contradicting the return to (0, 0).
Option D, North-West, would require a negative x and positive y displacement, again not matching the calculated coordinates.
Option E, South-East, would require positive x and negative y displacement, which is also inconsistent with the final coordinates.

Common Pitfalls:
Students sometimes stop tracking the path before the final movement or misinterpret one of the right turns, leading them to believe that Amit ends up at a corner of the square instead of the starting point. Another error is to focus only on total distance walked rather than displacement. Remember that displacement depends on net change in position, which can be zero even when a large distance has been covered in a closed loop.

Final Answer:
Amit returns exactly to his starting position, so he is At the original position.

Question 6

Raju walks 4 km towards the East from his starting point and then turns left to walk another 3 km towards the North. In which cardinal direction and at what straight-line distance is he now located from his initial position?

Accepted Answer

Introduction / Context:
Direction sense test questions check your ability to mentally track movements on an imaginary map and then identify the final position and direction of a person with respect to the starting point. In this problem, Raju first walks along the East direction and then turns left, which makes him face North. We are asked to determine both the resulting direction and the straight-line distance from his starting position, which is a classic right-angled triangle situation in basic geometry.
Given Data / Assumptions:

Raju starts from an initial point taken as the origin.
He walks 4 km towards the East.
He then turns left and walks 3 km, which means he now walks towards the North.
We use the standard convention: North is up, East is to the right, South is down and West is to the left on a map.
We assume he walks in straight lines and the turns are exact right angles.

Concept / Approach:
The movement described forms a right-angled triangle when we join the starting point and the final point. The leg along the East direction is 4 km and the leg along the North direction is 3 km. The shortest distance from the starting point to the final point is the hypotenuse of this triangle. By using the Pythagoras theorem, distance^2 = (horizontal displacement)^2 + (vertical displacement)^2. The direction is determined by noticing that the final point lies to the East and North of the origin, which corresponds to the North-East direction.
Step-by-Step Solution:
Step 1: Mark the starting point as O at coordinates (0, 0).
Step 2: Walking 4 km East takes Raju to point A with coordinates (4, 0).
Step 3: From facing East, a left turn means facing North. Walking 3 km North from A takes him to point B with coordinates (4, 3).
Step 4: Compute the straight-line distance OB using Pythagoras theorem: OB^2 = 4^2 + 3^2 = 16 + 9 = 25.
Step 5: Therefore, OB = √25 = 5 km, so the distance from the starting point to the final point is 5 km.
Step 6: Since the final coordinates (4, 3) are both positive, Raju is to the East and to the North of the starting point, which means he is in the North-East direction.

Verification / Alternative check:
A quick mental check is that the numbers 3, 4 and 5 form a well-known Pythagorean triplet. Whenever two perpendicular legs measure 3 and 4 units, the hypotenuse is 5 units. Here, one leg is 3 km and the other is 4 km, so 5 km is immediately reasonable. Also, because the path is “right then up” (East then North), the final position must lie in the North-East quadrant relative to the start. Both distance and direction are thus fully consistent with the detailed calculation.
Why Other Options Are Wrong:
South-West, 5 km is incorrect because Raju never travels towards the South or West overall; his net movement is towards the East and North. South-East, 5 km is wrong because there is no net movement towards the South; the final vertical movement is upwards. North-West, 5 km is also incorrect because there is no net displacement towards the West. North, 7 km is incorrect as the total displacement is not 7 km and also includes an Eastward component, so it cannot be purely North.
Common Pitfalls:
Students often confuse the direction after a left or right turn, especially when they do not explicitly imagine themselves facing the initial direction. Another common mistake is to simply add the distances 4 km and 3 km to get 7 km as the answer, forgetting that they are perpendicular displacements, not movements along the same straight line. Some learners also mislabel the quadrant and might claim South-East or North-West without plotting the final coordinates carefully. Drawing a small diagram with arrows for each move is a very reliable way to avoid these errors.
Final Answer:
Raju is finally at a point that is North-East, 5 km from his initial position.

Question 7

In a certain coded system of directions, the direction name South-East is replaced by North and the direction name North-East is replaced by West, and all other directions are renamed in the same cyclic pattern. According to this scheme, which direc…

Accepted Answer

Introduction / Context:
This problem belongs to the direction sense and coding category, where normal compass directions are renamed according to a given rule. Instead of moving a person on a map, we are told that specific directions are changed into new labels. Our task is to understand the pattern of renaming and then apply the same pattern to find what the original direction South will be called in this new coding system. Such questions primarily test logical reasoning and understanding of cyclic arrangements of the eight principal directions.
Given Data / Assumptions:

There are eight standard directions: North (N), North-East (NE), East (E), South-East (SE), South (S), South-West (SW), West (W) and North-West (NW).
In the new coded system, South-East is changed to North.
In the same coded system, North-East is changed to West.
The phrase “and so on” implies that the same cyclic rule applies to all remaining directions consistently.
We assume that the renaming follows a fixed step of rotation around the compass.

Concept / Approach:
To solve this, we list the eight directions in their natural clockwise order and try to interpret how the coding rule shifts one direction to another. By observing how South-East (SE) becomes North (N) and North-East (NE) becomes West (W), we can determine the shift in terms of positions along the circle. Once the exact shift is identified, we apply the same shift to South (S) to find its new name. This is essentially a problem of modular arithmetic on a circular arrangement.
Step-by-Step Solution:
Step 1: Write the eight directions in order: N, NE, E, SE, S, SW, W, NW.
Step 2: Assign position numbers for convenience: N(0), NE(1), E(2), SE(3), S(4), SW(5), W(6), NW(7).
Step 3: According to the code, SE (position 3) is renamed as N (position 0). This is a shift of -3 positions or equivalently +5 positions modulo 8 (because 3 + 5 = 8, which wraps to 0).
Step 4: Check the second mapping: NE (position 1) is renamed as W (position 6). This is also a shift of +5 positions (1 + 5 = 6), confirming the pattern.
Step 5: Apply the same +5 shift to South (S), which is at position 4. We compute 4 + 5 = 9; modulo 8, this is 1, which corresponds to North-East (NE).
Step 6: Therefore, South will be called North-East in this coded system.

Verification / Alternative check:
Another way is to visualize the directions on a circle and imagine that each direction is being relabelled by rotating five steps clockwise. Moving from SE to N involves “backing up” three positions or equivalently moving forward five positions. If we keep jumping five directions clockwise, NE indeed maps to W, and applying the same jump from S lands us on NE. This graphical intuition matches the position-counting method, confirming that North-East is the correct coded name for South.
Why Other Options Are Wrong:
South-West would require a different rotation step and does not match the observed mappings from SE and NE. South-East clearly cannot be the code for South because SE already has its own new name. North-West also does not follow the +5 shift pattern from S. East is similarly inconsistent with the shift that maps SE to N and NE to W. Only North-East preserves the same rotational behaviour for all the given cases.
Common Pitfalls:
A frequent mistake is to assume that directions are simply reversed or that North is always swapped with South, East with West, and so on. Here, however, the problem specifies only two mappings and asks the solver to infer the exact cyclic rule. Another pitfall is miscounting the steps around the circle or mixing up clockwise with anticlockwise movement. Writing the directions down in a clear ring and marking the step size prevents such errors and makes the pattern much easier to see.
Final Answer:
Under this renaming system, the direction South will be referred to as North-East.

Question 8

A driver leaves his village and first drives 20 km towards the North, where he stops for breakfast. He then turns left and drives another 30 km to stop for lunch, again turns left and drives 20 km to stop for evening tea, and finally turns left once…

Accepted Answer

Introduction / Context:
This problem is a classic direction sense question where a person travels in straight lines and makes a sequence of left turns. We must carefully track his path step by step and identify the direction of his last stretch of travel. Although there are multiple halts (breakfast, lunch, evening tea and supper), what really matters is the direction he is facing before and after each turn, especially just after evening tea when he starts his final drive to the town.
Given Data / Assumptions:

The driver first drives 20 km towards the North from the village.
He then turns left and drives 30 km, stopping for lunch.
After lunch, he again turns left and drives 20 km, stopping for evening tea.
After evening tea, he turns left once more and drives 30 km to reach the town.
All turns are 90 degree left turns, and the roads are straight.
We use the usual convention: facing North, left is West; facing West, left is South; facing South, left is East.

Concept / Approach:
To determine the final direction, it is helpful to track both the directions of travel and the relative orientation after each turn. Every left turn changes the facing direction by 90 degrees anticlockwise. We can either draw a simple diagram or simulate the movements using coordinates, but here the key question is not the final position but specifically the direction of the last movement starting from the evening tea point. Once we know what direction he was facing at that moment, applying one more left turn gives the direction of the final leg.
Step-by-Step Solution:
Step 1: From the village, the driver travels 20 km towards the North, so at the breakfast stop he is facing North.
Step 2: From facing North, he turns left. A left turn from North means he now faces West, and he drives 30 km to reach the lunch point.
Step 3: At the lunch point, he is facing West. He turns left again, so he now faces South, and travels 20 km to reach the evening tea point.
Step 4: At the evening tea point, he is facing South. The problem now asks for the direction of his drive after this stop.
Step 5: From facing South, a left turn will make him face East (because turning left from South is equivalent to rotating 90 degrees anticlockwise, which points to East).
Step 6: Therefore, his final drive from the evening tea halt to the town is in the East direction.

Verification / Alternative check:
We can verify the sequence by noting that three consecutive left turns effectively change a North-facing person to East-facing. Starting from North: first left gives West, second left gives South, and third left gives East. Because the driver makes these three left turns sequentially across the journey, his final direction of motion must be East. Drawing a simple square or rectangle with arrows labelled in order (North, West, South, East) will visually confirm the same pattern without any complicated calculations.
Why Other Options Are Wrong:
West would be the direction after only one left turn from North, which describes his movement to the lunch point, not the final leg. North is the initial direction, not the direction after three left turns. South is the direction he faces after the second left turn and is used for the leg between lunch and evening tea, not for the trip from evening tea to the town. North-East does not arise at any stage because all turns are exact right angles, so only the four main directions (North, East, South, West) appear in the path.
Common Pitfalls:
A common mistake is to mix up the number of left turns or to assume that three left turns bring a person back to the original direction, which is actually incorrect (four left turns return you to the original direction). Another error is to focus too much on distances to different stops instead of tracking orientation. Carefully listing the facing direction after each turn systematically avoids confusion and ensures that the final direction is identified correctly as East.
Final Answer:
After evening tea, the driver travels towards the East to reach the town.

Question 9

A marathon route starts from a fixed point and first goes 21 km towards the North. From there, the route turns towards the West and continues for 7 km, then turns towards the North again and continues for another 10 km. Finally, there is a right tur…

Accepted Answer

Introduction / Context:
This question describes the path of a marathon route using several straight-line segments and directional turns. The objective is to determine the net displacement of the finishing point with respect to the starting point. Such direction sense problems test your ability to convert a series of movements into a simplified overall position, often by visualizing or sketching a diagram and combining distances along the North–South and East–West axes separately.
Given Data / Assumptions:

The route begins at a starting point taken as the origin.
First, the route goes 21 km towards the North.
Next, it turns towards the West and continues for 7 km.
After that, it turns again towards the North and continues for 10 km.
Finally, there is a right turn and the route continues for 7 km until the finishing point.
Right turn from North means turning to the East, assuming standard compass conventions.
All distances are measured in straight lines and each turn is a 90 degree turn.

Concept / Approach:
We can treat this situation as movement on a coordinate grid. The North–South movements affect the vertical coordinate, while the East–West movements affect the horizontal coordinate. If a segment goes West and a later segment goes East by the same amount, these displacements can cancel each other. The net position is then found by summing all North movements and subtracting South movements, and similarly for East and West if needed. In this specific question, you will see that the West and East movements cancel out, leaving only a vertical displacement relative to the starting point.
Step-by-Step Solution:
Step 1: Assume the starting point is at (0, 0).
Step 2: The first movement is 21 km North, so the route reaches point A at (0, 21).
Step 3: From A, the route turns West and goes 7 km, reaching point B at (-7, 21).
Step 4: From B, the route turns North and travels 10 km, reaching point C at (-7, 31).
Step 5: From C, there is a right turn. From facing North, a right turn means facing East. The route then goes 7 km East to reach the finishing point D at (0, 31).
Step 6: Compare the coordinates of the starting point (0, 0) and finishing point (0, 31). There is no net East–West displacement (0 on both), but the finishing point is 31 km to the North of the starting point.

Verification / Alternative check:
Instead of plotting coordinates, we can track only the North–South and East–West components. Total Northward distance = 21 km + 10 km = 31 km. There is no Southward movement. Total Westward distance is 7 km, and later total Eastward distance is also 7 km, so these cancel each other. Therefore, the overall displacement is 31 km North from the start. This simple addition and cancellation method confirms the coordinate-based result and shows that the finishing point is exactly 31 km North of the starting position.
Why Other Options Are Wrong:
31 km South is wrong because the net vertical displacement is towards the North, not the South. 11 km North is incorrect because it ignores some of the Northward movement; it would arise only if 10 km of North movement were mistakenly subtracted. 11 km South is doubly incorrect, both in direction and in magnitude. 21 km North corresponds only to the first segment and does not account for the additional 10 km North travelled later in the route.
Common Pitfalls:
Students sometimes forget to include all Northward movements or fail to cancel out equal Eastward and Westward segments, leading to wrong net displacements. Another frequent error is mixing up left and right turns and therefore assigning the wrong direction to later segments. A quick sketch on paper with arrows and axes, or a small table tracking cumulative North–South and East–West distances, can greatly reduce such mistakes and make the solution straightforward.
Final Answer:
The finishing point of the marathon route is located 31 km North of the starting position.

Question 10

X and Y start from the same point. First, X walks 40 m towards the North, then turns to his left and walks 80 m towards the West, and finally turns to his right and walks 50 m towards the North. At the same time, Y walks 90 m straight towards the No…

Accepted Answer

Introduction / Context:
This direction sense question involves two people, X and Y, starting from the same point but taking different paths. We are asked to compare their final positions. Instead of simply finding where each one ends up relative to the origin, we must determine where Y is located relative to X. Such problems are very common in aptitude tests and require careful tracking of both paths and then comparing the coordinates or relative positions at the end.
Given Data / Assumptions:

X and Y start from the same initial point.
X walks 40 m towards the North.
Then X turns left and walks 80 m, which means he goes towards the West.
Next, X turns right and walks 50 m, which again takes him towards the North.
Meanwhile, Y walks 90 m straight towards the North from the starting point.
All turns are 90 degree turns, and paths are straight.
We use the usual orientation: North is up, East is right, South is down and West is left.

Concept / Approach:
It is efficient to place the starting point at the origin of a coordinate system and track the movements of X and Y separately. Vertical movements (North–South) change the y-coordinate, while horizontal movements (East–West) change the x-coordinate. Once we know the final coordinates of both X and Y, we can compare them to find the relative displacement of Y with respect to X. The sign of the x-coordinate difference will immediately show whether Y is to the East or West of X and by how many metres.
Step-by-Step Solution:
Step 1: Let the starting point be (0, 0).
Step 2: Track X. X walks 40 m North to reach (0, 40).
Step 3: From facing North, a left turn takes X towards the West. He walks 80 m West to reach (-80, 40).
Step 4: From facing West, a right turn makes him face North again. He walks 50 m North to reach (-80, 90). So X's final coordinates are (-80, 90).
Step 5: Track Y. Y walks 90 m North in a straight line from the starting point to reach (0, 90). So Y's final coordinates are (0, 90).
Step 6: To find where Y is relative to X, compare coordinates: X is at (-80, 90) and Y is at (0, 90). The y-coordinates are the same, so they are horizontally aligned.
Step 7: The x-coordinate of Y (0) is 80 units greater than the x-coordinate of X (-80). This means Y is 80 m to the East of X.

Verification / Alternative check:
We can also interpret the movements qualitatively. From the start, both X and Y eventually reach the same North–South level of 90 m because X moves 40 m North, then an additional 50 m North, and Y moves directly 90 m North. However, X also moves 80 m West, while Y stays on the original vertical line. Therefore, Y must be exactly 80 m to the East of X along a horizontal line. This matches the coordinate method and confirms that the separation between them is purely East–West, with Y lying to the East.
Why Other Options Are Wrong:
30 m East or West is incorrect because the actual horizontal separation between their x-coordinates is 80 m, not 30 m. Saying Y is 80 m to the West of X reverses their relative positions because X has moved West while Y has not, so Y cannot be further West than X. Claiming Y is 10 m to the South of X is wrong because both have the same North–South coordinate (90 m), so there is no vertical difference at all; they are on the same horizontal line.
Common Pitfalls:
A typical mistake is to compare each person's path to the origin but not to each other, which can lead to incorrect inferences about relative locations. Another common error is misinterpreting left and right turns, especially when there are multiple turns for the same person. Drawing a simple diagram and labelling the positions after each move or using coordinates is the best strategy for avoiding confusion and quickly deducing the relative position.
Final Answer:
Y is finally located 80 m to the East of X.

Question 11

Priya cycles 5 km towards the North from her starting point, then turns right to cycle 4 km towards the East. From there she turns right again and cycles 5 km towards the South, and finally she turns to her right once more and cycles 6 km. Where is …

Accepted Answer

Introduction / Context:
This question describes a cyclist, Priya, travelling along a rectangular-like path with several right turns. We are asked to determine her final position with respect to the starting point. Problems of this type involve tracking stepwise movements in the North–South and East–West directions and then computing the net displacement. Recognizing when segments cancel each other is key to simplifying the final answer quickly.
Given Data / Assumptions:

Priya starts from a fixed point.
She cycles 5 km towards the North.
Then she turns right and cycles 4 km towards the East.
After that, she turns right again and cycles 5 km towards the South.
Finally, she turns to her right and cycles 6 km.
All turns described as “right” are 90 degree turns, and all stretches are straight-line segments.
We use the usual convention that from facing North, a right turn leads to East; from East, right leads to South; and from South, right leads to West.

Concept / Approach:
We can model Priya's movement on a coordinate grid. North–South displacements affect the vertical coordinate, and East–West displacements affect the horizontal coordinate. Some movements may cancel out: for example, going 5 km North and then 5 km South returns her to the same North–South level. The final horizontal position can then be deduced by accumulating the Eastward and Westward displacements. This method avoids confusion and makes the final position clear without needing complex geometry.
Step-by-Step Solution:
Step 1: Assume Priya starts at (0, 0).
Step 2: She cycles 5 km North to reach (0, 5). She is now facing North.
Step 3: She turns right from North, which means she now faces East, and cycles 4 km to reach (4, 5).
Step 4: From facing East, she turns right again to face South and cycles 5 km, reaching (4, 0).
Step 5: From facing South, she turns right once more to face West and cycles 6 km, finally reaching (-2, 0).
Step 6: The starting point is (0, 0), and the final position is (-2, 0). This means she is 2 km to the West of the starting point.

Verification / Alternative check:
We can verify by comparing net North–South and East–West movements separately. Total Northward distance is 5 km and total Southward distance is also 5 km, so North–South displacement is zero. For East–West, she goes 4 km East, then 6 km West. Net horizontal displacement = 6 km West − 4 km East = 2 km West. Since the vertical displacement is zero, her final position must be exactly 2 km West of the starting point, confirming the coordinate calculation.
Why Other Options Are Wrong:
2 km East reverses the actual direction; Priya ends up West, not East, of the start. 10 km West and 10 km East greatly exaggerate the net movement and ignore the cancellations that occur in the North–South and East–West directions. 6 km North would require a net positive vertical displacement, which does not happen here because the 5 km North and 5 km South movements cancel each other out completely.
Common Pitfalls:
Some learners mistakenly add all distances without considering direction, leading to incorrect large values such as 10 km or more. Others may misinterpret right turns, especially after multiple turns, or forget that opposite movements cancel out. Drawing the path on graph paper or mentally tracking the coordinates after each step is a reliable technique that reduces errors significantly in such direction sense questions.
Final Answer:
Priya's final position is 2 km West of her starting point.

Question 12

An auto-rickshaw picks up a passenger and first travels 6.5 km towards the North from the starting point. It then turns left and rides for 1.5 km towards the West, turns again towards the South and rides 2.5 km, and finally turns left once more and …

Accepted Answer

Introduction / Context:
This direction sense problem involves an auto-rickshaw moving along a set of straight segments with left turns, and we must determine the final position relative to the starting point. The path consists of movements towards North, West, South and finally East (due to the last left turn). By converting the description into horizontal and vertical displacements, we can compute how far and in which direction the auto ends up from its initial location.
Given Data / Assumptions:

The auto starts from an initial point.
It travels 6.5 km towards the North.
It then turns left and rides 1.5 km, which from facing North means towards the West.
Next, it turns towards the South and rides 2.5 km.
Finally, it turns left again and rides 1.5 km.
We assume all turns are 90 degree turns and all segments are along straight roads.
Standard orientation is used: North is up, East is right, South is down and West is left.

Concept / Approach:
The best approach is to treat each segment as a vector on a coordinate grid. Vertical displacements (North and South) affect the y-coordinate, while horizontal displacements (East and West) affect the x-coordinate. Often, equal movements in opposite directions can cancel each other out. Tracking this step by step allows us to easily find the net position. In this problem, the Westward and Eastward movements are equal, so only the net North–South displacement remains.
Step-by-Step Solution:
Step 1: Place the starting point at coordinates (0, 0).
Step 2: The auto first travels 6.5 km North to reach (0, 6.5).
Step 3: From facing North, a left turn means facing West. Riding 1.5 km West brings it to (-1.5, 6.5).
Step 4: It then turns towards the South and rides 2.5 km, reaching (-1.5, 4.0). The North–South displacement is now 4.0 km above the origin.
Step 5: Finally, from facing South, a left turn makes it face East. Riding 1.5 km East brings it to (0, 4.0).
Step 6: The final coordinates are (0, 4.0), while the starting point is (0, 0). This shows that the auto is 4 km to the North of the starting point and has no net East–West displacement.

Verification / Alternative check:
We can check by only considering net vertical and horizontal movements. Vertically, it goes 6.5 km North and then 2.5 km South, giving a net of 6.5 − 2.5 = 4 km North. Horizontally, it goes 1.5 km West and later 1.5 km East, so these cancel each other out completely, leaving zero net East–West movement. Therefore, the auto must be directly North of the starting point at a distance of 4 km, which confirms our coordinate-based result.
Why Other Options Are Wrong:
9 km North and 9 km South are impossible because the total distance travelled is not even that large in a single direction, and we have both North and South movements that partially cancel. 4 km South is incorrect because the net vertical movement is clearly towards the North, not the South. 1.5 km West would imply that Westward motion is not cancelled by Eastward motion, but the path includes equal West and East segments of 1.5 km each, resulting in zero horizontal displacement.
Common Pitfalls:
Many candidates lose track of direction when multiple left turns are involved, or they forget that some segments undo earlier movements. Another common mistake is to try to add all distances numerically without considering direction, which is not meaningful for displacement questions. Drawing a diagram with the distances labelled or maintaining a simple table of cumulative North–South and East–West components is an effective way to avoid confusion and arrive at the correct answer quickly.
Final Answer:
The auto is now located 4 km North of its starting position.

Question 13

Rahul leaves his home and first walks 5 km towards the East. He then turns in the South-East direction and walks 10 km, after which he turns in the North-East direction and walks another 10 km. Finally, he moves straight towards the North for 10 km.…

Accepted Answer

Introduction / Context:
This is a more advanced direction sense question because it involves movements not only along the main North–South–East–West directions but also along diagonal directions, namely South-East and North-East. We must determine the final direction of Rahul from his starting point after several such moves. To solve it accurately, we need to interpret diagonal movements as equal components along two perpendicular axes and then combine all horizontal and vertical displacements to identify the final quadrant in which Rahul lies relative to his home.
Given Data / Assumptions:

Rahul starts from his home, which we treat as the origin.
He walks 5 km towards the East initially.
He then turns towards the South-East direction and walks 10 km.
Next, he turns towards the North-East direction and walks another 10 km.
Finally, he moves 10 km straight towards the North.
South-East is taken as a diagonal direction equally inclined between South and East, and North-East is equally inclined between North and East.
We assume ideal 45 degree diagonal directions so that each diagonal movement has equal North–South and East–West components.

Concept / Approach:
To handle diagonal movements, each 10 km step in a 45 degree direction is broken into two perpendicular components using basic trigonometry. For a 45 degree diagonal, the horizontal and vertical components are equal and can be taken as 10 / √2 km each. We then treat all movements as vectors, sum the East–West components and the North–South components separately, and examine the sign and relative size of the net components. If both net components are positive (East and North), the final direction will be North-East, and similarly for other quadrants.
Step-by-Step Solution:
Step 1: Place home at (0, 0). After walking 5 km East, Rahul is at (5, 0).
Step 2: Walking 10 km South-East means moving 10 / √2 km East and 10 / √2 km South. Numerically, 10 / √2 is approximately 7.07 km.
Step 3: From (5, 0), add East component +7.07 and South component −7.07 to get approximately (12.07, −7.07).
Step 4: Walking 10 km North-East from this point adds +7.07 km East and +7.07 km North. So the new position is about (12.07 + 7.07, −7.07 + 7.07) = (19.14, 0.00).
Step 5: Finally, walking 10 km North adds 10 km to the y-coordinate, giving a final position of roughly (19.14, 10).
Step 6: At the end, Rahul's x-coordinate is positive (East) and his y-coordinate is positive (North), which clearly places him in the North-East direction relative to the starting point.

Verification / Alternative check:
Even without heavy calculation, we can reason qualitatively. Rahul first moves East, then diagonally South-East (adding East and South components), then diagonally North-East (adding East and North components that cancel the earlier South component), and finally moves North. The Southward and Northward diagonal components cancel approximately, leaving an overall strong Eastward displacement and a final Northward component from the last move. Hence, his net displacement is to the East and North of the origin, which must correspond to North-East. A rough sketch using equal diagonals at 45 degrees will visually confirm this conclusion.
Why Other Options Are Wrong:
West is impossible because Rahul moves predominantly East or diagonal with an East component in every stage; there is no move with a net West component. East alone ignores the clear Northward movement at the end that lifts him above the starting level. North-West would require a West component, which does not exist here. South-East would place him below the starting point, but the final 10 km North move makes his net vertical displacement positive (North), not negative (South). Thus only North-East matches both the qualitative and quantitative analysis.
Common Pitfalls:
A common error is to treat diagonal movements as if they occur entirely in one direction, for example, counting 10 km South-East as 10 km South and 10 km East simultaneously, which overestimates the displacement. Another mistake is to focus on the last movement alone and ignore the cumulative effect of earlier diagonals on the final position. When dealing with such questions, it is helpful to break diagonals into components or at least to sketch approximate 45 degree lines to see in which quadrant the endpoint lies.
Final Answer:
Rahul is finally located in the North-East direction from his starting point (home).

Question 14

Two rugby players, A and B, start running from the same point on the pitch. Player A runs 20 m towards the South, then turns to his left and runs 26 m. Meanwhile, Player B runs 12 m towards the West, then 6 m towards the South, and then turns to his…

Accepted Answer

Introduction / Context:
In this question, two rugby players move on the same field along different routes, and we are asked to find the relative position of Player A with respect to Player B at the end. This is a typical direction sense and relative position problem. Instead of focusing on where each player is relative to the origin, we specifically compare their final coordinates to see whether A is North, South, East or West of B and by what distance.
Given Data / Assumptions:

Both Player A and Player B start from the same point on the pitch.
Player A runs 20 m towards the South and then turns left to run 26 m.
Player B runs 12 m towards the West, then 6 m towards the South, and then turns left to run 38 m.
All turns are right-angle turns, and all distances are straight-line segments.
We use the standard convention: from South, a left turn faces East, and from West, a left turn faces South.
We choose a coordinate system with North–South as the vertical axis and East–West as the horizontal axis.

Concept / Approach:
To solve this systematically, we assign coordinates to each final position. We place the common starting point at (0, 0). Vertical movements change the y-coordinate (positive for North, negative for South), while horizontal movements change the x-coordinate (positive for East, negative for West). After computing the final coordinates of both players, we compare them. If Player A has a smaller y-coordinate than Player B but the same x-coordinate, A will be directly South of B by the difference in their y-values.
Step-by-Step Solution:
Step 1: Let the starting point of both players be (0, 0).
Step 2: Track Player A. He runs 20 m South, reaching (0, -20).
Step 3: From facing South, a left turn means facing East. Running 26 m East, he reaches (26, -20). So Player A's final coordinates are (26, -20).
Step 4: Track Player B. He first runs 12 m West, reaching (-12, 0).
Step 5: Next, he runs 6 m South to reach (-12, -6).
Step 6: From facing South, a left turn means facing East. Running 38 m East from (-12, -6) takes him to (-12 + 38, -6) = (26, -6). So Player B's final coordinates are (26, -6).
Step 7: Compare the positions: A is at (26, -20) and B is at (26, -6). They have the same x-coordinate (26), so they are vertically aligned. A's y-coordinate is -20, while B's is -6, which is 14 units higher. Therefore, Player A is 14 m South of Player B.

Verification / Alternative check:
We can also reason qualitatively. Both players eventually end up on the same vertical line because Player A moves East 26 m and Player B net moves West 12 m and then East 38 m, which results in 26 m East of the origin. For vertical movement, A goes 20 m South, whereas B effectively goes only 6 m South, so A is 14 m further South than B (20 − 6 = 14). This confirms that A is directly South of B by 14 m, matching the coordinate-based calculation.
Why Other Options Are Wrong:
26 m South or 26 m North are incorrect magnitudes; 26 m is the horizontal distance from the starting point, not the vertical separation between the players. 14 m North of B would reverse the direction; instead of A being above B, we found that A is lower (more South). 38 m East is unrelated to the vertical question being asked and simply reflects one of the segments run by B, not the relative position between A and B.
Common Pitfalls:
One common error is ignoring the sign of the vertical displacement and assuming that the larger raw number corresponds to the correct answer. Another is confusing left and right turns or mixing up which player made which move, which leads to incorrect coordinates. Writing down each intermediate point and carefully computing the net displacements is a robust way to avoid such mistakes. A simple sketch of the field with axes and labelled points for A and B also makes the relative position very clear.
Final Answer:
Player A is located 14 m South of Player B.

Question 15

An insect starts from a point and walks 15 cm towards the East. It then turns to its right and walks 20 cm, turns right again and walks 4 cm, then turns towards the North and walks 20 cm, and finally turns to its left and walks 2 cm. Where is the in…

Accepted Answer

Introduction / Context:
This direction sense question describes an insect walking along straight segments with right turns and a specific absolute movement towards the North. We must find the insect's final position relative to its starting point in terms of East–West displacement. The trick is to interpret the sequence of right turns correctly and track horizontal and vertical displacements separately, then compare the final coordinate with the origin.
Given Data / Assumptions:

The insect starts from an initial point (the origin).
It walks 15 cm towards the East.
It then turns to its right and walks 20 cm, which from facing East means walking towards the South.
Next, it turns right again and walks 4 cm, which from facing South means walking towards the West.
Then it turns towards the North (absolute direction) and walks 20 cm.
Finally, it turns to its left and walks 2 cm; from facing North, left indicates the West direction.
All distances are measured along straight lines and right/left turns are 90 degrees.

Concept / Approach:
We will track the insect's path on a coordinate grid where East–West displacements affect the x-coordinate and North–South displacements affect the y-coordinate. Some segments may cancel the vertical displacement (such as equal South and North movements), leaving only horizontal displacement. At the end, we compare the final coordinates to the origin to see whether the insect is East or West of the starting point and by how much in centimetres.
Step-by-Step Solution:
Step 1: Assume the starting point is (0, 0).
Step 2: Walking 15 cm East takes the insect to (15, 0); it is facing East.
Step 3: From facing East, a right turn faces South. Walking 20 cm South leads to (15, -20).
Step 4: From facing South, a right turn faces West. Walking 4 cm West takes it to (11, -20).
Step 5: The insect then turns towards North (absolute direction) and walks 20 cm, moving to (11, 0). The Southward and Northward movements cancel.
Step 6: From facing North, a left turn faces West. Walking 2 cm West moves the insect to (9, 0).
Step 7: The final position is (9, 0) compared to the starting point (0, 0), so the insect is 9 cm to the East of its starting point.

Verification / Alternative check:
We can sum the horizontal and vertical movements separately. Horizontally, the insect moves 15 cm East, 4 cm West, and 2 cm West. Net horizontal displacement = 15 − 4 − 2 = 9 cm East. Vertically, it moves 20 cm South and 20 cm North, which cancel to zero. Therefore, the insect ends up directly East of the starting point by 9 cm. This matches the coordinate approach and confirms that there is no North–South displacement in the final position.
Why Other Options Are Wrong:
21 cm East or West ignores the net cancellations and overestimates the displacement. 9 cm West would only occur if the Westward movements exceeded the Eastward movement, which is not the case here. 4 cm North assumes there is a net vertical displacement, but the 20 cm South and 20 cm North movements cancel exactly, leaving no net North–South shift. Hence only 9 cm East is consistent with the described path.
Common Pitfalls:
Students may misinterpret the change from relative directions (right/left) to absolute directions (North) and then back to relative directions (left from North), leading to incorrect final directions. Another common error is to add distances without considering direction or to forget to subtract movements in opposite directions. Drawing a simple diagram, marking each turn, and writing cumulative East–West and North–South components is a robust strategy to avoid such mistakes.
Final Answer:
The insect is now located 9 cm East of its starting point.

Question 16

Sonal is standing to the North of Amar and also to the West of Mahi. Based on this information about their relative positions on a standard map, in which direction is Mahi standing with respect to Amar?

Accepted Answer

Introduction / Context:
This is a relative position direction sense question involving three people: Amar, Sonal and Mahi. We are given information about Sonal's location relative to both Amar and Mahi, and we are asked to find Mahi's direction with respect to Amar. Such questions are solved by placing one person at a reference point (often Amar), plotting the position of the second person (Sonal) using the given relationships and then deducing the position of the third person (Mahi).
Given Data / Assumptions:

Sonal is standing to the North of Amar.
Sonal is also standing to the West of Mahi.
We are asked: in which direction is Mahi standing with respect to Amar?
We assume the standard orientation for directions: North is up, East is right, South is down and West is left.
We assume that the descriptions “North of” and “West of” refer to straight-line projections on a simple map (no diagonal exceptions).

Concept / Approach:
To simplify, we fix the position of Amar at a convenient reference point, such as the origin of a coordinate system. Then we place Sonal relative to Amar and Mahi relative to Sonal. From there, we compute the relative position of Mahi with respect to Amar. If the resulting coordinates show that Mahi is to the East and North of Amar, the direction from Amar to Mahi is North-East; similarly we could get North-West, South-East or South-West depending on the signs of the horizontal and vertical differences.
Step-by-Step Solution:
Step 1: Assume Amar is at point A with coordinates (0, 0).
Step 2: Sonal is to the North of Amar. Place Sonal at point S directly above A, say at (0, 1), meaning she is somewhere North of Amar.
Step 3: Sonal is also to the West of Mahi. This means Mahi must be to the East of Sonal. Place Mahi at point M to the right of S, for example at (1, 1).
Step 4: Now compare the coordinates of Mahi and Amar. Amar is at (0, 0) and Mahi is at (1, 1). Mahi is 1 unit to the East (positive x-direction) and 1 unit to the North (positive y-direction) of Amar.
Step 5: Being both East and North of Amar places Mahi in the North-East direction relative to Amar.

Verification / Alternative check:
We can also reason without coordinates. If Sonal is North of Amar, draw Amar at a point and Sonal somewhere directly above. If Sonal is West of Mahi, draw Mahi somewhere to the right of Sonal. Now compare Amar and Mahi visually: Amar is at the lower left, Mahi is at the upper right. From Amar, you must move up (North) and then to the right (East) to reach Mahi, which is exactly the North-East direction. This geometric sketch confirms the coordinate-based conclusion.
Why Other Options Are Wrong:
South-West would mean Mahi is below and to the left of Amar, which contradicts Sonal being North of Amar and West of Mahi. North-West would place Mahi above and to the left of Amar, but we know Mahi must be to the East of Sonal, who is directly above Amar. South-East would put Mahi below and to the right of Amar, which again conflicts with the fact that Sonal is North of Amar and West of Mahi. East alone ignores the necessary Northward shift indicated by Sonal being North of Amar while also West of Mahi.
Common Pitfalls:
A frequent source of confusion is mixing up whether to draw positions relative to Amar or relative to Sonal. Some candidates incorrectly assume that if Sonal is North of Amar and West of Mahi, then Mahi is South-East of Amar, which happens only if the relationships are misinterpreted. Taking a moment to sketch the situation and labelling each person clearly prevents such mistakes and makes the North-East relationship obvious.
Final Answer:
Mahi is standing in the North-East direction with respect to Amar.

Question 17

Starting from a point, a person travels 3 km towards the East and then turns left to travel 4 km towards the North. After that he again turns to his left by 45° and continues to walk straight. In which direction is he now facing after this final tur…

Accepted Answer

Introduction / Context:
This question tests understanding of both right-angle and non-right-angle turns in direction sense. The person first moves along two perpendicular directions (East then North) and then makes a further 45 degree left turn from his current facing direction. We are not asked to find his position, but specifically to determine the direction he is facing after the last turn. Correctly interpreting left turns and angles is crucial here.
Given Data / Assumptions:

The person starts from an initial point.
He travels 3 km towards the East.
He then turns left and travels 4 km, which implies moving towards the North.
After that, he again turns to his left by 45 degrees.
We must find the direction he is facing after this 45 degree left turn.
We assume standard compass directions and that 45 degree turns lie halfway between two main cardinal directions.

Concept / Approach:
The key is to track the orientation of the person, not his exact position. Initially, he faces East. A left turn from East gives North. Another left turn of 90 degrees from North would give West, but here he turns only 45 degrees to the left, which means he ends up facing exactly halfway between North and West, that is, North-West. Remember that turning left means rotating anticlockwise on the compass, and a 45 degree turn corresponds to moving to a diagonal direction between two main directions.
Step-by-Step Solution:
Step 1: At the start, the person begins by walking 3 km towards the East. Therefore, his initial facing direction is East.
Step 2: From facing East, he makes a left turn. A 90 degree left turn from East points towards North. He then walks 4 km North, so his current facing direction is North.
Step 3: Now, from facing North, he again turns to his left, but this time the turn is 45 degrees, not a full 90 degrees.
Step 4: Visualize the compass: to the left (anticlockwise) of North is West. The direction exactly halfway between North and West is North-West, which is at a 45 degree angle between them.
Step 5: Because he rotated 45 degrees anticlockwise from North, his new facing direction is therefore North-West.

Verification / Alternative check:
A simple compass diagram can verify this. Mark East, North and West on a circle. From East to North is a 90 degree anticlockwise turn, which matches the first left turn. From North, another full 90 degree left turn would reach West, but this problem specifies only a 45 degree left turn, so his direction lies exactly halfway between North and West. That intermediate direction is labelled North-West on the standard eight-direction compass, confirming our reasoning without any coordinate calculations.
Why Other Options Are Wrong:
North-East is to the right of North (clockwise) and would result from a right turn, not a left one. South-East and South-West are below the East–West line and would require turning around past the South direction, which is not mentioned here. East would correspond to his initial facing direction, which he has clearly changed twice by turning left. Thus, only North-West matches a 45 degree left turn from a North-facing orientation.
Common Pitfalls:
A common error is to treat the 45 degree left turn as if it were another 90 degree left turn, which would lead to West instead of North-West. Another mistake is confusing clockwise and anticlockwise rotations when interpreting left and right. To avoid these pitfalls, always imagine yourself facing the given direction and then mentally rotate in the specified sense by the required angle, or quickly sketch a compass with the angles marked at 45 degree intervals.
Final Answer:
After turning left by 45 degrees from North, the person is facing towards the North-West direction.

Question 18

A man is initially facing East. He turns 60 degrees in the anticlockwise (left) direction and then again turns another 120 degrees in the same anticlockwise direction. After completing these two turns, in which direction is he finally facing?

Accepted Answer

Introduction / Context:
This is a pure turning and orientation problem without any distances. A man starts facing East and takes two anticlockwise turns: one of 60 degrees and another of 120 degrees. We must find his final facing direction. Such questions test understanding of angles on a compass, the meaning of anticlockwise rotation, and the fact that the net effect of multiple rotations is the sum of the angles in the same direction.
Given Data / Assumptions:

The man initially faces East.
He turns 60 degrees in the anticlockwise (left) direction.
Then he turns another 120 degrees in the same anticlockwise direction.
We must determine his final facing direction after both turns.
We assume a full circle is 360 degrees and directions are spaced at 90 degree intervals (East, North, West, South, back to East).

Concept / Approach:
When a person turns through multiple angles in the same rotational direction, the total rotation is just the sum of the angles. Here, both rotations are anticlockwise, so we add 60 degrees and 120 degrees to get 180 degrees of anticlockwise rotation. Starting from East, an anticlockwise rotation of 90 degrees leads to North, and a further 90 degrees (total 180 degrees) leads to West. Therefore, his final direction is West. We do not need to worry about intermediate diagonal directions because the net rotation is exactly 180 degrees, corresponding to one of the main cardinal directions.
Step-by-Step Solution:
Step 1: Start by marking East as the initial direction.
Step 2: The man first turns 60 degrees anticlockwise from East. This places him somewhere between East and North, closer to East, but we do not need to label this intermediate direction precisely yet.
Step 3: He then turns another 120 degrees anticlockwise from his current orientation.
Step 4: The total anticlockwise rotation is 60 + 120 = 180 degrees from his original facing direction (East).
Step 5: On a compass, a 90 degree anticlockwise rotation from East leads to North, and another 90 degrees (making 180 degrees total) leads to West.
Step 6: Therefore, after the two turns, he ends up facing West.

Verification / Alternative check:
We can also think in terms of cardinal points as angle measures: East can be treated as 0 degrees, North as 90 degrees, West as 180 degrees and South as 270 degrees, all measured anticlockwise. Starting at East (0 degrees), a 180 degree anticlockwise rotation brings him to angle 180 degrees, which is West. Since the net rotation is exactly 180 degrees, there is no need to consider fractional or diagonal directions such as North-East or South-East. This confirms that West is the correct final direction.
Why Other Options Are Wrong:
East would require either no rotation or a multiple of full 360 degree turns, which we do not have here. North-West would correspond to a 135 degree anticlockwise rotation from East, not 180 degrees. South-East is 315 degrees anticlockwise from East (or 135 degrees clockwise), which does not match the given rotations. North is only 90 degrees anticlockwise from East, which occurs halfway through his full rotation, not at the end. Thus, West is the only direction consistent with a total of 180 degrees anticlockwise rotation from East.
Common Pitfalls:
A common mistake is to add angles incorrectly or to forget that both turns are in the same anticlockwise direction, leading to subtraction instead of addition. Some learners also misplace the directions on the circle, mixing up the order of North, West and South. Drawing a simple circle with East on the right, North at the top, West on the left and South at the bottom, and then marking the 180 degree anticlockwise rotation, is an excellent way to visualize the correct final direction quickly.
Final Answer:
After the two anticlockwise turns, the man is finally facing towards the West.

Question 19

A man walks 7 km towards the South from a starting point and then turns to his left to walk 5 km. From there he turns to his right and walks another 7 km. In which direction is he now located from the starting point?

Accepted Answer

Introduction / Context:
This direction sense question involves three straight segments of walking with left and right turns. We must determine the final direction of the man with respect to his starting position. The path includes South, East and South again, leading to a net displacement in a particular quadrant. The question does not ask for exact distance, only the direction from the starting point, which simplifies the computation.
Given Data / Assumptions:

The man starts from a fixed point.
He walks 7 km towards the South.
He then turns left and walks 5 km.
From there, he turns right and walks another 7 km.
We assume each left and right turn is a 90 degree turn.
Standard direction conventions are used: from facing South, left is East and right is West; from facing East, right is South, and so on.

Concept / Approach:
We can track the man's movement on a coordinate plane by splitting his travel into horizontal (East–West) and vertical (North–South) components. Because he moves South twice and East once, there will be net South and net East displacements. The combination of these two components will place him in one of the four quadrants relative to the starting point, and we can identify that quadrant by noting that both the South and East components are positive in magnitude.
Step-by-Step Solution:
Step 1: Assume the starting point is at (0, 0).
Step 2: The man walks 7 km South, reaching (0, -7); he is now facing South.
Step 3: From facing South, a left turn means facing East. Walking 5 km East brings him to (5, -7).
Step 4: At this point, he faces East. From facing East, a right turn makes him face South again. Walking another 7 km South takes him to (5, -14).
Step 5: Comparing with the origin (0, 0), his final coordinates (5, -14) indicate he is 5 km to the East and 14 km to the South of the starting point.
Step 6: Being both East and South of the origin places him in the South-East direction relative to the starting point.

Verification / Alternative check:
We do not need the exact distance to determine the direction, but we can check the components. Total Southward distance is 7 km + 7 km = 14 km. Total Northward distance is zero, so net Southward movement is 14 km. Total Eastward distance is 5 km and total Westward distance is zero, so net Eastward movement is 5 km. Since there is both Southward and Eastward displacement, the final direction must be South-East. Drawing the path with arrows further confirms that he is located in the quadrant that is both below and to the right of the starting point.
Why Other Options Are Wrong:
West would require a net displacement to the left of the origin, but there is no Westward movement here. South alone ignores the Eastward shift of 5 km; he is not directly below the starting point. North-East would place him above the origin, which contradicts the fact that all vertical motion is towards the South. East alone ignores the substantial Southward component and would only be correct if there were no net vertical displacement.
Common Pitfalls:
A common mistake is to misinterpret the left turn from South, thinking it leads to West instead of East. Another is to overlook the second Southward movement or to assume that opposite vertical motions cancel, even when there is no Northward movement. Keeping a simple tally of North–South and East–West movements, or sketching the path, helps avoid these issues and makes the South-East answer obvious.
Final Answer:
The man is now located in the South-East direction from the starting point.

Question 20

Amar drives 20 km towards the East from his home to reach a hospital. From the hospital, he turns left and travels 30 km, and then again turns left and travels 20 km to reach his school. How far is his school from his home (the starting point)?

Accepted Answer

Introduction / Context:
Originally framed in terms of the distance from the hospital, this question is best interpreted as a standard direction sense and distance problem comparing Amar's school and home. Amar travels in a rectangular path with two left turns, and we must determine the straight-line distance between his home and his final destination, the school. This is a classic application of coordinate tracking and the Pythagoras theorem in a real-life driving scenario.
Given Data / Assumptions:

Amar starts from his home.
He drives 20 km towards the East to reach the hospital.
From the hospital, he turns left and drives 30 km, which means he goes towards the North.
Then he again turns left and drives 20 km to reach his school, which takes him towards the West.
We are asked for the straight-line distance between his school and his home.
All turns are 90 degree left turns and roads are straight.
We use the standard direction convention: from East, left is North; from North, left is West.

Concept / Approach:
We track Amar's movements on a coordinate plane, representing home as the origin. After his route, the school's coordinates can be calculated. Once we have the coordinates of both home and school, the distance between them is simply the length of the straight line joining these points. Given that Amar's path forms the sides of a right-angled triangle (one leg vertical and one leg horizontal), the Pythagoras theorem can be used to find the distance: distance^2 = (horizontal difference)^2 + (vertical difference)^2.
Step-by-Step Solution:
Step 1: Place Amar's home at (0, 0).
Step 2: He drives 20 km East to the hospital, reaching (20, 0).
Step 3: From facing East, a left turn is towards North. He drives 30 km North to reach (20, 30).
Step 4: From facing North, another left turn means he now faces West. Driving 20 km West takes him to (0, 30), which is the location of his school.
Step 5: Home is at (0, 0) and the school is at (0, 30). The horizontal difference is 0, and the vertical difference is 30 km.
Step 6: Therefore, the straight-line distance between his home and his school is simply 30 km.

Verification / Alternative check:
We can visualize his journey as forming a rectangle: one side is 20 km East–West, and the other side is 30 km North–South. However, because the last 20 km West leg exactly cancels the first 20 km East leg in terms of horizontal position, the school ends up directly North of the home. That means the shortest distance between home and school is just the vertical side of 30 km, not the diagonal. This matches the coordinate calculation, confirming that the required distance is 30 km.
Why Other Options Are Wrong:
25 km and 27 km are typical distractors that might arise from guessing or misapplying Pythagoras to incorrect legs of a triangle, but they do not match the actual geometry. 35 km is too large and would require an additional, uncompensated displacement. 20 km would only be correct if the school lay directly East or West of home at the same North–South level, which is not the case here, since the school is 30 km North of home after the journey.
Common Pitfalls:
Candidates sometimes mistakenly compute the distance between the hospital and the school, or misread the question, instead of focusing on home-to-school distance. Another mistake is to add all the distances (20 + 30 + 20) or to use Pythagoras on non-perpendicular legs, leading to incorrect answers. Carefully plotting the points and noting that the first and last legs cancel horizontally are key steps for avoiding these errors.
Final Answer:
Amar's school is 30 km away from his home in a straight line.

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