Question 1

Direction sense — taxi driver's current facing A taxi goes 10 km North, turns left 5 km (West), waits, then turns right and goes 10 km (North). After 25 km total, which direction is he facing now?

Accepted Answer

Introduction / Context:We are asked for the orientation after the final leg.Given Data / Assumptions:Final movement is northward; waiting does not affect heading.Final Answer:North

Question 2

Direction sense — Mr. A's displacement from X (multi-turn) From X: East 80 m → right 40 m (South) → right 80 m (West) → left 20 m (South) → left 80 m (East) → left 60 m (North). How far and in which direction from X is he now?

Accepted Answer

Introduction / Context:Add vector components to obtain final displacement.Given Data / Assumptions:Endpoint computed at (80, 0).Concept / Approach:Magnitude 80 m, bearing due East.Final Answer:80 m towards East

Question 3

Direction sense — school relative to mall Mall is 250 m North-West of market; school is 250 m South-West of market. In which direction is the school from the mall?

Accepted Answer

Introduction / Context:Points share the same West offset but different North/South offsets relative to market.Given Data / Assumptions:Mall: (−d, +d); School: (−d, −d).Concept / Approach:Vector from mall to school = (0, −2d) ⇒ due South.Final Answer:South

Question 4

Direction sense — shadow to the right at 8:00 am A person walking at 8:00 am observes his shadow to his right. In which direction is he walking?

Accepted Answer

Introduction / Context:In the morning, the Sun is in the East and shadows fall toward the West.Given Data / Assumptions:Shadow to the right means the person's right-hand side is toward the West.Concept / Approach:If right side points West, the person faces South (since facing South gives right = West).Final Answer:South

Question 5

Direction sense — car's facing after two right turns A car starts (towards North), goes 8 km, turns right 9 km (East), then turns right and stops. Which direction does it face now?

Accepted Answer

Introduction / Context:Two right turns rotate heading by 180°.Given Data / Assumptions:North → right = East; East → right = South.Final Answer:South

Question 6

In a certain direction–sense code, South-East is renamed as North, North-East is renamed as West and so on following the same pattern. Under this redefined system of directions, what will the original direction West be called?

Accepted Answer

Introduction:This is a classic direction–sense coding problem. The usual eight directions (North, North-East, East, South-East, South, South-West, West, North-West) are renamed according to a fixed pattern. We are told how two directions are renamed, and we must infer the rule and then find what the original direction West will be called under this code. The question checks your ability to work with circular arrangements and rotational mappings.
Given Data / Assumptions:We are given the following coded information:• South-East is called North.• North-East is called West.• The phrase "and so on" indicates that the same rotation rule applies to all eight directions.• We assume the standard order of directions: North, North-East, East, South-East, South, South-West, West, North-West arranged clockwise.
Concept / Approach:The idea is to treat the eight directions as points on a circle, equally spaced at 45 degree intervals. A renaming such as "South-East becomes North" means that wherever the original South-East lies on the compass, it is now given the new label North. In other words, we are rotating labels around the compass. If we can find how many steps clockwise (or anticlockwise) this mapping represents, we can apply the same shift to West and obtain its new coded name.
Step-by-Step Solution:Step 1: List the standard directions in order (clockwise): North (0), North-East (1), East (2), South-East (3), South (4), South-West (5), West (6), North-West (7).Step 2: We are told that South-East becomes North. In index form, 3 is renamed as 0. This is a shift of +5 steps (3 + 5 = 8, which wraps to 0 mod 8).Step 3: Check this shift with the second clue. North-East is index 1. Apply the same +5 shift: 1 + 5 = 6, which corresponds to West. That matches the statement "North-East becomes West", so the rotation rule is confirmed.Step 4: Now apply this same +5 step rotation to the original direction West. West has index 6.Step 5: Compute 6 + 5 = 11. Taking modulo 8, 11 mod 8 = 3, which is South-East in our original direction list.Step 6: Therefore, West will be renamed as South-East in this code language.
Verification / Alternative check:We can also view the rotation as moving every label 135 degrees clockwise (since 3 to 0 is a shift of 3 steps anticlockwise or 5 steps clockwise). If North moves to West, West moves to South-East, and South-East moves to North, we see a consistent pattern around the compass. Each direction is simply relabelled by the same rotation, so West must indeed map to South-East.
Why Other Options Are Wrong:North-East and North-West would correspond to different rotational shifts that are not supported by the two given examples. South-West would be correct only if every direction were moved a different number of steps, which would break the uniform coding pattern. South is also not reached from West by the confirmed +5 step rotation, so it cannot be the coded name for West.
Common Pitfalls:Candidates sometimes confuse which is being rotated: the compass or the names. The safe way is to fix the compass directions and rotate only the labels, or equivalently to treat the mapping as an index shift. Another common error is to use a +3 or -5 shift without verifying it against both given clues. Always confirm your rotation with all provided examples before using it on the required direction.
Final Answer:Under this coding pattern, the original direction West is renamed as South-East.

Question 7

One morning just after sunrise, Suresh was standing facing a vertical pole. The shadow of the pole fell exactly to his right-hand side. In this situation, towards which cardinal direction was Suresh facing?

Accepted Answer

Introduction:This direction–sense question uses the position of the Sun and the direction of a shadow to determine the direction a person is facing. The scene is set "one morning after sunrise", which immediately tells us the approximate position of the Sun in the sky. By combining that basic fact with the information about where the shadow falls relative to Suresh, we can work out his facing direction.
Given Data / Assumptions:• Time: One morning after sunrise.• Suresh is facing a pole.• The shadow of the pole falls exactly to his right side.• We use the basic rule: In the morning, in most reasoning questions set in India, the Sun is taken to be in the East and shadows are cast towards the West.
Concept / Approach:Shadows always fall in the direction opposite to the Sun. In the morning the Sun is in the East, therefore any vertical object on level ground will have its shadow cast towards the West. The key idea is to align Suresh so that his right-hand side lies along the direction of the pole's shadow, which is West. Once we know that Suresh's right points West, we can deduce the direction in which his face is pointing using the usual compass orientation of left and right.
Step-by-Step Solution:Step 1: Since it is morning, assume the Sun is in the East.Step 2: Therefore, the shadow of the pole must fall towards the West.Step 3: We are told that the pole's shadow falls exactly to Suresh's right. So Suresh's right-hand side is aligned with the West direction.Step 4: Now recall the basic orientation rule: when a person faces North, the East lies to their right; when they face South, the West lies to their right.Step 5: Because Suresh's right side is West, the only possibility is that Suresh is facing South.Step 6: Hence, Suresh must be facing South.
Verification / Alternative check:If Suresh were facing North, his right side would be East, which contradicts the fact that the shadow is to his right and lies in the West. If he faced East, his right would be South; if he faced West, his right would be North. None of these match the condition that his right coincides with West. Therefore, South is the only direction consistent with the given data.
Why Other Options Are Wrong:East and West do not match the left–right relationship described. "Data is inadequate" is incorrect because we have enough information: time of day, Sun position, and the side on which the shadow falls. North cannot work either, since that would place West on Suresh's left, not on his right.
Common Pitfalls:Many learners misremember the morning rule and think of the Sun as being in the West because they imagine sunset rather than sunrise. Another common mistake is to confuse left and right relative to the person's facing direction. Drawing a simple compass diagram and a stick-figure facing each direction is often sufficient to avoid such errors.
Final Answer:Given the Sun's position in the morning and the direction of the pole's shadow, Suresh must be facing South.

Question 8

Rahul placed his wristwatch flat on a table in such a way that at 6:00 P.M. the hour hand points exactly towards the North. Keeping the watch fixed in that position, in which direction will the minute hand be pointing at 9:15 P.M.?

Accepted Answer

Introduction:This direction–sense problem uses a clock face as a reference for directions. Rahul rotates the clock so that at a specific time (6:00 P.M.) the hour hand points to a given cardinal direction (North). The orientation of the entire dial is thus fixed. We are then asked to find the direction of the minute hand at another time (9:15 P.M.) with respect to the same orientation.
Given Data / Assumptions:• At 6:00 P.M., the hour hand points to North.• The watch lies flat and stays fixed on the table after it is placed.• The question asks for the direction of the minute hand at 9:15 P.M., measured against the same compass directions.• We use the standard positions: on a normal clock face, 12 is at the top, 3 at the right, 6 at the bottom, and 9 at the left.
Concept / Approach:At 6:00 P.M., the hour hand normally points at the 6 on the dial, which is downward relative to 12. Rahul rotates the entire clock so that this downward direction (towards 6) now points North. That rotation also fixes new compass directions for 12, 3, and 9. After that, we simply determine where the minute hand points at 9:15 P.M. on the dial and translate that into the corresponding compass direction.
Step-by-Step Solution:Step 1: At 6:00 P.M., in a standard orientation, the hour hand points to the 6, which is vertically down from the centre.Step 2: Rahul places the watch so that this downward direction now points to the North. Therefore, the 6-mark direction corresponds to North.Step 3: Since 12 is opposite 6, the 12-mark direction now corresponds to South.Step 4: On the usual clock, 3 lies to the right and 9 to the left of 12. With 12 now pointing South, 3 points West and 9 points East (because the entire dial has been rotated 180 degrees compared with the normal North-at-12 assumption).Step 5: At 9:15 P.M., the minute hand points exactly at the 3 on the dial (because it is 15 minutes past the hour).Step 6: As established, the 3-mark direction in this orientation points towards the West.Step 7: Therefore, at 9:15 P.M., Rahuls minute hand points West.
Verification / Alternative check:We can verify by imagining the dial: if the hour hand at 6 points North, then the dial is effectively upside down compared to the usual North-at-12 orientation. That makes 3 become West and 9 become East. The minute hand at 15 minutes always aims at 3, independent of the hour hand. Hence, West is consistent and there is no ambiguity in the direction.
Why Other Options Are Wrong:South and North refer to directions associated with the 12 and 6 marks under this rotated arrangement, not with the 3 mark. South-East and North-West would require intermediate diagonal positions that the minute hand does not occupy at exactly 9:15 P.M. Therefore, they cannot be correct. West is the only direction that matches the 3-mark in the rotated dial.
Common Pitfalls:A frequent mistake is to assume 12 always points North and then work from that, forgetting that the entire clock has been rotated. Others confuse the hour hand's position at 9:15 P.M. with the minute hand's position, even though the question asks only about the minute hand. Keeping the dial orientation fixed after the initial rotation and focusing on the correct hand avoids such errors.
Final Answer:With the clock oriented so that the 6-mark points North, the minute hand at 9:15 P.M. points towards the West.

Question 9

Two cars start simultaneously from opposite ends of a straight main road that is 150 km long. The first car travels 25 km along the main road, then turns right and goes 15 km, then turns left and travels another 25 km before finally returning back t…

Accepted Answer

Introduction:This is a direction–sense cum distance problem involving two cars starting from opposite ends of a straight main road. One car leaves the main road, moves along side roads with right and left turns, and then returns to the main road. The other car travels only a short distance along the main road. We must track the path of each car in a coordinate-style way and then compute the distance between their positions when the first car has just returned to the main road and the second car has covered 35 km.
Given Data / Assumptions:• Length of the main road between the two starting points is 150 km.• Car 1: moves 25 km along the main road, then 15 km after a right turn, then 25 km after a left turn, then returns to the main road.• Car 2: due to a breakdown, travels only 35 km along the main road from its end towards the other car.• We assume the main road is straight and runs East–West, and both cars start at the same time from opposite ends, heading towards each other.
Concept / Approach:The best method is to place the main road on a coordinate axis. Let the western end be at x = 0 and the eastern end at x = 150. Both cars start respectively at these points and initially travel along the x-axis. Car 1 then leaves the road, moves in a perpendicular direction, and later returns to the road at a certain x-coordinate. Car 2 continues only along the main road. Once we know the final x-coordinates of both cars on the main road at the required instant, the distance between them is simply the difference of those coordinates.
Step-by-Step Solution:Step 1: Place Car 1 at the western end of the road at (0, 0). It travels 25 km towards the east along the main road to (25, 0).Step 2: At (25, 0), Car 1 turns right. Since it has been travelling east, a right turn takes it towards the south. It travels 15 km to (25, -15).Step 3: From there it turns left. Facing south, a left turn takes it towards the east. It travels a further 25 km to (50, -15).Step 4: It then returns to the main road. The main road is along the x-axis (y = 0), so it must travel 15 km due north (from y = -15 to y = 0). Thus it rejoins the main road at (50, 0).Step 5: Meanwhile, Car 2 starts from the eastern end (150, 0) and runs 35 km west along the same road. Its position is therefore (115, 0).Step 6: At the moment described, Car 1 is at x = 50, y = 0 and Car 2 is at x = 115, y = 0.Step 7: The distance between them is the difference in x-coordinates: 115 - 50 = 65 km.
Verification / Alternative check:Note that the “out and back” southward detour of Car 1 (down 15 km then back up 15 km) does not change its final position on the main road, which only depends on the east–west components. Also, Car 2 has not left the main road at all. Hence the distance must be along the road and equals 65 km, matching the simple coordinate difference we calculated.
Why Other Options Are Wrong:Values such as 75 km, 80 km or 85 km would require miscalculating the east–west displacement of Car 1 or Car 2, or mistakenly including the temporary southward movement of Car 1 in the final separation. The distance between the two points on a straight line is always the absolute difference between their coordinates, which is 65 km here.
Common Pitfalls:Many students get distracted by the extra turns of Car 1 and incorrectly add the 15 km detour to the separation between the cars. Others assume that both cars travel the full 150 km, forgetting that Car 2 moves only 35 km due to a breakdown. Drawing a simple diagram with coordinates helps keep track of each movement without confusion.
Final Answer:At the described moment, the two cars are separated by a distance of 65 km.

Question 10

Point K is located 40 m to the South-West of point L. Point M is located 40 m to the South-East of point L. With respect to point K, in which direction does point M lie?

Accepted Answer

Introduction:This direction–sense question involves three points placed at fixed distances and directions: K, L and M. We are told where K and M lie relative to L, and we must determine the direction of M with respect to K. The displacements are along diagonals (South-West and South-East), so a simple coordinate approach helps clarify their relative positions.
Given Data / Assumptions:• K is 40 m to the South-West of L.• M is 40 m to the South-East of L.• South-West means equally towards the South and West from L; South-East similarly means equally towards the South and East.• We are asked: In which direction is M from K?
Concept / Approach:We place L at the origin of a coordinate system. South is taken as negative y, North as positive y, East as positive x and West as negative x. Moving South-West from L moves us some equal distance in the negative x and negative y directions. Moving South-East from L moves us the same distance in positive x and negative y. Since the magnitudes are equal (40 m in each diagonal case), we can reason with equal components without worrying about the exact trigonometric values.
Step-by-Step Solution:Step 1: Place L at coordinates (0, 0).Step 2: A 40 m move towards South-West from L can be represented as going some distance “a” units west (negative x) and the same distance “a” units south (negative y). Thus, K can be represented approximately as (−a, −a).Step 3: Similarly, a 40 m move towards South-East from L can be represented as going “a” units east (positive x) and “a” units south (negative y). Thus, M is at (a, −a).Step 4: To find the direction of M from K, compute the displacement from K to M. This displacement vector is (a − (−a), −a − (−a)) = (2a, 0).Step 5: A displacement of (2a, 0) has a positive x-component and zero y-component, which means it is purely towards the East.Step 6: Therefore, M lies due East of K.
Verification / Alternative check:You can also visualize L at the top of an isosceles triangle, with K and M forming the base corners at equal distances downwards. The base of that triangle is horizontal. From the left base point (K) you move horizontally to the right to reach the right base point (M). A horizontal move from left to right corresponds directly to the East direction.
Why Other Options Are Wrong:West would correspond to moving from right to left, which is the direction of K from M, not M from K. South would require a downward displacement, which does not happen when going from K to M. North-East would involve both an upward and rightward movement, whereas there is no vertical change between K and M. South-East also has a downward component, but here the y-coordinates are equal, so that option is not appropriate.
Common Pitfalls:Candidates often confuse the phrase "direction of M from K" with "direction of K from M". Direction questions are not symmetric: East of K means West of M. Another common error is to focus only on the words South-West and South-East and incorrectly pick South, without carefully computing the relative position. A quick sketch of the three points usually makes the situation clear.
Final Answer:With respect to K, point M lies directly to the East.

Question 11

Rasik walks 20 m towards the North, then turns right and walks 30 m, then turns right again and walks 35 m. After that he turns left and walks 15 m, and finally he turns left once more and walks 15 m. From his starting position, in which direction i…

Accepted Answer

Introduction:This is a typical direction–sense tracking problem in which a person makes several moves with specified distances and directions, including right and left turns. We need to follow Rasik's path step by step, map his movement on a simple coordinate system, and finally determine his net displacement from the starting point, both in magnitude and direction.
Given Data / Assumptions:• Rasik walks 20 m towards North.• Then turns right and walks 30 m.• Then turns right and walks 35 m.• Then turns left and walks 15 m.• Finally turns left and walks 15 m.• We assume flat ground and standard compass directions: North up, East right, South down, West left.
Concept / Approach:The most reliable approach is to treat Rasik's path like movement on the x–y plane, with North as positive y, East as positive x, South as negative y, and West as negative x. Each turn changes his facing direction by 90 degrees left or right. By updating both the facing direction and the coordinates after each segment, we can compute his final position relative to the starting point and then measure the net displacement.
Step-by-Step Solution:Step 1: Start at (0, 0), facing North. Walking 20 m North takes Rasik to (0, 20).Step 2: Turning right from North means he now faces East. Walking 30 m East takes him to (30, 20).Step 3: Turning right from East means he now faces South. Walking 35 m South decreases the y-coordinate: 20 − 35 = −15, so his position becomes (30, −15).Step 4: Turning left from South means he now faces East again. Walking 15 m East increases the x-coordinate: 30 + 15 = 45, giving (45, −15).Step 5: Turning left from East now makes him face North. Walking 15 m North increases the y-coordinate from −15 to 0, so his final position is (45, 0).Step 6: The starting point is (0, 0). The difference is (45, 0), which is purely 45 m to the East.
Verification / Alternative check:We can see that Rasik's final y-coordinate is 0, which means he is back on the same East–West line as his starting point. All net displacement occurs along the East–West axis. His eastward distances were 30 + 15 = 45 m, and he never moved west, so he is exactly 45 m East of the starting point. This matches our coordinate calculation perfectly.
Why Other Options Are Wrong:Options like 15 m West or 30 m West contradict the fact that he never walked westwards. Similarly, 30 m East underestimates his eastward movement. Any answer involving West as the direction is incorrect because every sideways move after the first right turn was towards the East, not the West. The correct final displacement is 45 m in the East direction.
Common Pitfalls:Students often get confused by multiple left and right turns and lose track of the direction they are facing at each step. Some also incorrectly combine distances without separating north–south and east–west components. A quick diagram or a small table listing direction, step length and updated coordinates after each turn greatly reduces these mistakes.
Final Answer:Rasik is finally located 45 m East of his starting position.

Question 12

A man walks 5 km towards the South and then turns to his right. After walking 3 km, he turns left and walks 4 km. He then goes back 10 km straight along the same line. From his starting place, in which direction is he now located?

Accepted Answer

Introduction:This direction–sense problem describes a person walking in several legs, with some left and right turns, and finally retracing a path in the opposite direction. We must determine the man's final direction from the starting point. The key idea is to treat each segment as a vector and keep track of both direction and distance using a coordinate system.
Given Data / Assumptions:• First, the man walks 5 km towards the South.• He then turns to the right and walks 3 km.• Next, he turns left and walks 4 km.• Finally, he goes back 10 km straight, meaning directly opposite to his then current facing direction.• We assume standard compass directions and level ground.
Concept / Approach:We place the starting point at the origin of an x–y coordinate system: North as positive y, East as positive x, South as negative y, and West as negative x. By updating his position after each move and turn, we can find his final coordinates. The direction from the origin to this final point tells us in which quadrant he is (for example, North-East, North-West), which is what the question asks for.
Step-by-Step Solution:Step 1: Start at (0, 0) facing South. Walking 5 km South takes him to (0, −5).Step 2: Turning right from South makes him face West. Walking 3 km West moves him to (−3, −5).Step 3: Turning left from West makes him face South again. Walking 4 km South takes him to (−3, −9).Step 4: He then "goes back 10 km straight". At this point he is facing South, so going back means turning around and walking 10 km towards the North.Step 5: From (−3, −9), moving 10 km North increases the y-coordinate: −9 + 10 = 1. His final position is (−3, 1).Step 6: Relative to the origin, he is 3 km West (negative x) and 1 km North (positive y). This lies in the North-West quadrant.
Verification / Alternative check:We can summarize the net movement: along the north–south axis he moved 5 km South, then 4 km further South, and finally 10 km North. The combined effect is 9 km South and 10 km North, giving a net 1 km North. Along the east–west axis he moved only 3 km West, with no eastward movement, giving a net 3 km West. The combination of North and West components confirms the direction as North-West.
Why Other Options Are Wrong:South-East would require net movement South and East, which is inconsistent with a final y-coordinate of +1 and x-coordinate of −3. Pure South would need no net northward movement, but we have a net movement of 1 km North. West alone would require no net northward displacement. North-East would involve positive x and positive y, whereas we have negative x and positive y. Only North-West matches the coordinate signs.
Common Pitfalls:Many learners forget that "goes back 10 km straight" means reversing direction along the same line, not continuing forward. Others lose track of left and right turns, especially when the person is facing South or West. Drawing a labelled sketch with each leg marked is a simple and effective way to avoid such directional mistakes.
Final Answer:From the starting place, the man is finally located in the North-West direction.

Question 13

A man is initially facing North-West. He turns 90 degrees in the clockwise direction, then 180 degrees in the anticlockwise direction and then another 90 degrees in the same (anticlockwise) direction. After these three turns, in which direction is h…

Accepted Answer

Introduction:This question focuses purely on direction changes caused by clockwise and anticlockwise turns. The man starts facing one of the inter-cardinal directions (North-West) and then makes three successive rotations. We must keep track of his facing direction after each turn and finally identify the direction he faces after all the turns are complete.
Given Data / Assumptions:• Initial facing direction: North-West.• First turn: 90 degrees clockwise.• Second turn: 180 degrees anticlockwise.• Third turn: 90 degrees in the same (anticlockwise) direction as the second turn.• We assume the standard eight directions spaced at 45 degree intervals: N, NE, E, SE, S, SW, W, NW.
Concept / Approach:Each 45 degree step around the compass moves you to an adjacent direction. Since the turns are multiples of 90 degrees, each 90 degree rotation equals two 45 degree steps. It is convenient to imagine the directions arranged in a circle and to count steps clockwise or anticlockwise from the starting point. By updating the facing direction after each turn, we arrive at the final facing direction.
Step-by-Step Solution:Step 1: List the eight directions clockwise: North, North-East, East, South-East, South, South-West, West, North-West.Step 2: The man starts facing North-West, which is the last direction in this list.Step 3: First turn: 90 degrees clockwise from North-West. Ninety degrees is two steps of 45 degrees. From North-West, one clockwise step goes to North, and the second step goes to North-East. So after the first turn he faces North-East.Step 4: Second turn: 180 degrees anticlockwise from North-East. One hundred eighty degrees equals four steps of 45 degrees. From North-East, going anticlockwise four steps leads to South-West.Step 5: Third turn: 90 degrees anticlockwise from South-West (same direction as the second turn). Ninety degrees equals two steps anticlockwise. From South-West, two anticlockwise steps move us to South-East.Step 6: Therefore, after all the turns, the man is facing South-East.
Verification / Alternative check:We can double check by noting net rotation. The first turn is +90 degrees (clockwise). The second is −180 degrees (anticlockwise), and the third is −90 degrees (anticlockwise). The total rotation is +90 − 180 − 90 = −180 degrees relative to the starting direction (North-West). Turning 180 degrees anticlockwise from North-West leads directly to South-East, confirming our earlier step-by-step reasoning.
Why Other Options Are Wrong:South and South-West both lie adjacent to South-East but require a different net rotation. East would be reached from North-West by a 135 degree clockwise rotation, which is not the net effect here. North is neither 180 degrees nor the described set of rotations away from North-West. Only South-East matches the cumulative 180 degree anticlockwise change.
Common Pitfalls:Students sometimes mix up clockwise and anticlockwise directions, or they forget that the second and third turns are in the same anticlockwise direction. Others attempt to track only the net angle without checking it against intermediate orientations, leading to sign errors. Carefully counting 45 degree steps around a drawn compass diagram is a robust way to avoid mistakes.
Final Answer:After all the turns, the man is facing towards the South-East direction.

Question 14

Amit starts walking with his back towards the Sun. After some time, he turns left, then turns right, and then turns left once again. In which direction is he walking now?

Accepted Answer

Introduction:This problem involves both the position of the Sun and a sequence of left and right turns. Amit starts with his back towards the Sun, but the time of day is not specified, so the Sun's direction may be East (morning) or West (evening). After three turns, we must work out in which direction he is walking. Because the time is ambiguous, the answer is expressed as a set of possible directions.
Given Data / Assumptions:• Amit begins with his back towards the Sun.• After walking for some time, he turns left.• Then he turns right.• Then he turns left again.• The problem does not specify morning or evening, so the Sun could be in the East (after sunrise) or West (before sunset).
Concept / Approach:If Amit's back is towards the Sun, he is facing directly opposite the Sun. In the morning, the Sun is in the East, so he would be facing West. In the evening, the Sun is in the West, so he would be facing East. We can represent both cases separately and then apply the same sequence of turns (left, then right, then left) to each starting direction. The final direction will be 90 degrees to the left of his original facing direction in either case.
Step-by-Step Solution:Case 1 (Morning): Sun in the East.Step 1: If the Sun is in the East, Amit's back is towards East and he faces West.Step 2: Starting facing West, a left turn points him South.Step 3: From South, a right turn makes him face West again.Step 4: From West, a final left turn makes him face South.So in the morning case he ends up facing South.Case 2 (Evening): Sun in the West.Step 5: If the Sun is in the West, Amit's back is towards West and he faces East.Step 6: Starting facing East, a left turn points him North.Step 7: From North, a right turn makes him face East again.Step 8: From East, a final left turn makes him face North.So in the evening case he ends up facing North.
Verification / Alternative check:In both cases, notice that the sequence left, then right, then left is equivalent to a net left turn of 90 degrees relative to the original direction. Turning left (+90), then right (−90), then left (+90) gives a net rotation of +90 degrees. So the final direction is always 90 degrees to the left of the starting direction: left of West is South, and left of East is North. This confirms our step-by-step reasoning.
Why Other Options Are Wrong:Options involving East or West as final directions would be correct only if the net rotation were 0 or 180 degrees. Here the net rotation is +90 degrees left, not 0 or 180. Options that mix West or East with the correct directions are misleading because the starting direction itself is East or West, but not the final one. Only "North or South" correctly captures the two possibilities depending on whether it is morning or evening.
Common Pitfalls:Candidates sometimes assume a specific time (usually morning) and ignore the other possibility, leading to only one direction (South). Others mis-handle left and right turns when the person is facing West or East, which are more error prone than when facing North. The safest approach is to consider both Sun positions and track the turns slowly or by drawing a small compass diagram.
Final Answer:Depending on whether the Sun is in the East or in the West, Amit is finally walking towards the North or South direction.

Question 15

I am facing South. I turn right and walk 20 m, then I turn right again and walk 10 m. Next, I turn left and walk 10 m and then, after turning right, I walk 20 m. Finally, I turn right once more and walk 60 m. From my starting point, in which directi…

Accepted Answer

Introduction:This direction–sense problem describes several moves with precise distances and multiple right and left turns. We need to determine in which direction the person is from the starting point after all movements are completed. Using a coordinate plane and tracking the direction after every turn allows us to find the final position and its direction relative to the origin.
Given Data / Assumptions:• Initial facing direction: South.• First, turn right and walk 20 m.• Turn right again and walk 10 m.• Turn left and walk 10 m.• Turn right and walk 20 m.• Turn right again and walk 60 m.• Standard compass directions and flat ground are assumed.
Concept / Approach:We treat the movement as motion on an x–y plane. North corresponds to positive y, South to negative y, East to positive x and West to negative x. Right and left turns specify 90 degree rotations relative to the current facing direction. By updating both the position and facing direction step by step, we can compute the final coordinates and interpret them as a direction from the starting point.
Step-by-Step Solution:Step 1: Start at (0, 0) facing South.Step 2: Right turn from South points West. Walking 20 m West moves to (−20, 0).Step 3: Right turn from West points North. Walking 10 m North moves to (−20, 10).Step 4: Left turn from North points West. Walking 10 m West moves to (−30, 10).Step 5: Right turn from West points North. Walking 20 m North moves to (−30, 30).Step 6: Right turn from North points East. Walking 60 m East increases the x-coordinate: −30 + 60 = 30, so we reach (30, 30).Step 7: The starting point is (0, 0) and the final point is (30, 30). Thus the person is 30 m to the East and 30 m to the North of the starting position.
Verification / Alternative check:Because both the x and y coordinates of the final position are positive and equal (30, 30), the final point lies in the first quadrant, exactly diagonally from the origin along the North-East line. The distance is not requested, only the direction, so recognising that both components are positive immediately tells us that the direction from the starting point is North-East.
Why Other Options Are Wrong:North alone would require no net East–West displacement, but we have 30 m East. East alone would require no net North–South displacement, but we have 30 m North. North-West would require a negative x-component (towards West), which is not the case. South-East would require positive x but negative y, also inconsistent with our final coordinates. Only North-East matches both positive coordinates.
Common Pitfalls:It is easy to get disoriented when turning from West or South and misidentify right and left. Others forget to update the facing direction correctly at each stage. Keeping a small table of (current direction, movement, new direction, new coordinates) after every instruction or drawing a stepwise path on graph paper significantly reduces the risk of errors.
Final Answer:From the starting point, the person is finally located towards the North-East direction.

Question 16

One morning after sunrise, Nivedita and Niharika were talking to each other face to face at Dalphin crossing. Niharika's shadow was observed to be exactly to the right of Nivedita. In this situation, in which direction was Niharika facing?

Accepted Answer

Introduction:This direction–sense question involves shadows, face-to-face positioning, and relative orientation. We are told that it is morning after sunrise and that the shadow of one person is exactly to the right of the other. Using the knowledge that morning shadows fall towards the West, and that the two people are facing each other, we must determine in which direction Niharika is facing.
Given Data / Assumptions:• Time: Morning after sunrise.• Location: Dalphin crossing (a typical four-way crossing).• Nivedita and Niharika are standing face to face.• Niharika's shadow is exactly to the right of Nivedita.• We use the standard reasoning convention: in the morning, the Sun is taken to be in the East, so shadows fall towards the West.
Concept / Approach:In the morning, the Sun is in the East and shadows are cast towards the West. The phrase "Niharika's shadow was exactly to the right of Nivedita" means that, from Nivedita's perspective, the direction West is on her right side. Once we know which direction lies on Nivedita's right, we can deduce which way she is facing. Since they stand face to face, we then infer Niharika's facing direction as the opposite of Nivedita's.
Step-by-Step Solution:Step 1: In the morning, the Sun is in the East. Therefore, the shadow of any vertical object (or person) falls towards the West.Step 2: Niharika's shadow is to the right of Nivedita. Thus, from Nivedita's point of view, her right-hand side coincides with the West direction.Step 3: We now ask: When is West on your right? If you face North, your right side is East. If you face South, your right side is West.Step 4: Therefore, Nivedita must be facing South (since her right side is West).Step 5: The two women are facing each other. If Nivedita faces South, then Niharika, standing opposite her, must be facing North.Step 6: Hence, Niharika is facing the North direction.
Verification / Alternative check:We can also reason by drawing a small diagram: mark the four directions at the crossing. Place Nivedita facing South so that her right side is West. Place Niharika opposite her facing North. Draw a ray from the East (Sun) passing behind Niharika to form a shadow towards the West. That shadow falls on the right side of Nivedita, matching the description. Any other starting orientation fails to align the right side with the Westward shadow.
Why Other Options Are Wrong:If Niharika faced South, then Nivedita would face North and Nivedita's right would be East, not West. Facing East or West for Niharika would not produce the described arrangement with the shadow on Nivedita's right-hand side. "Data is inadequate" is incorrect because the combination of morning time, face-to-face positioning, and shadow direction is sufficient to deduce a unique answer.
Common Pitfalls:Students sometimes accidentally place the Sun in the West because they think of sunset rather than sunrise. Others forget that the two people are face to face and try to assign the same facing direction to both. Always check carefully which side (left or right) a direction lies on relative to a given facing, and use a sketch if needed.
Final Answer:In this situation, Niharika was facing towards the North direction.

Question 17

Person "P" walked 1 km towards the South, then turned 90 degrees anticlockwise and walked 2 km. He then turned left and walked 1 km, turned right and walked 2 km, and finally turned 90 degrees anticlockwise and walked 3 km. How far is he from his st…

Accepted Answer

Introduction:This direction–sense question describes a path involving several turns, including explicit 90 degree anticlockwise rotations. The aim is to find the straight-line distance from the starting point after all the movements are completed. By tracking the person's position through a coordinate method, we can determine the final displacement and thus the required distance.
Given Data / Assumptions:• P walks 1 km towards the South.• Then he turns 90 degrees anticlockwise (ACW) and walks 2 km.• Then he turns left and walks 1 km.• Then he turns right and walks 2 km.• Finally he turns 90 degrees anticlockwise and walks 3 km.• Flat terrain and standard compass directions are assumed.
Concept / Approach:We assign coordinates: North as positive y, South as negative y, East as positive x, West as negative x. We also track the current facing direction at each step. A 90 degree anticlockwise turn is equivalent to a left turn when facing North, but we must always interpret it relative to the current facing direction. By successively updating the facing direction and coordinates, we end with a final coordinate from which the distance to the origin is easily computed using the Pythagorean theorem.
Step-by-Step Solution:Step 1: Start at (0, 0) facing South. Walking 1 km South moves P to (0, −1).Step 2: He then turns 90 degrees anticlockwise from South. On a compass, anticlockwise from South takes us to East.Step 3: Walking 2 km East from (0, −1) moves him to (2, −1).Step 4: He now turns left from East, which makes him face North. Walking 1 km North takes him to (2, 0).Step 5: Next he turns right from North, which sends him facing East again. Walking 2 km East from (2, 0) moves him to (4, 0).Step 6: Finally, he turns 90 degrees anticlockwise from East, which points him North. Walking 3 km North from (4, 0) takes him to (4, 3).Step 7: The starting point is (0, 0) and the final point is (4, 3), which is a classic 3–4–5 right triangle.
Verification / Alternative check:The net east–west movement is 4 km East and no movement West, so the x-displacement is +4 km. The net north–south movement is 1 km North (from step 4) plus 3 km North (from step 6) minus 1 km South (from step 1), giving 3 km North. The straight-line distance from (0, 0) to (4, 3) is sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5 km, confirming that the final distance is 5 km.
Why Other Options Are Wrong:Distances such as 4 km or 3 km correspond to only one side of the right triangle, not the hypotenuse. A distance of 2 km or 0 km would imply either a much smaller displacement or that he returned exactly to the starting point, which is not supported by the net east and north movement we computed. Only 5 km correctly reflects both components of his travel.
Common Pitfalls:Students sometimes interpret anticlockwise turns as always meaning a turn to the left without considering the current facing direction, which can be misleading when your starting direction is not North. Others confuse the order of turns. Writing down a small table with columns for current direction, action, new direction, and new coordinates is a systematic way to avoid such mistakes.
Final Answer:After all the movements, P is 5 km away from his starting point.

Question 18

In a symbolic direction notation, "A x B" means A is to the South of B, "A + B" means A is to the North of B, "A % B" means A is to the East of B and "A - B" means A is to the West of B. In the expression P % Q + R - S, in which direction is S locat…

Accepted Answer

Introduction:This question uses symbolic notation to describe relative directions between points or persons. Different symbols represent "south of", "north of", "east of" and "west of". We must interpret a combined expression P % Q + R - S and then determine the direction of S with respect to Q. The key is to decode each relation carefully and then place all points on a coordinate grid.
Given Data / Assumptions:• A x B: A is to the South of B.• A + B: A is to the North of B.• A % B: A is to the East of B.• A - B: A is to the West of B.• Expression: P % Q + R - S.• We are asked: In which direction is S with respect to Q?
Concept / Approach:We interpret each relation pairwise. For example, P % Q means P is to the East of Q. Working left to right, we express all points in terms of Q. Once we know the relative positions of P, R and S on an x–y coordinate grid, we can compute the displacement from Q to S and identify the corresponding direction (such as North-East, South-West, etc.).
Step-by-Step Solution:Step 1: Decode P % Q. The symbol % means "to the East of", so P is to the East of Q.Step 2: Decode Q + R. The symbol + means "to the North of", so Q is to the North of R. Equivalently, R is to the South of Q.Step 3: Decode R - S. The symbol - means "to the West of", so R is to the West of S. Equivalently, S is to the East of R.Step 4: Introduce coordinates. Place Q at (0, 0) for convenience.Step 5: Since Q is North of R, R must be South of Q, so we can place R at (0, −1).Step 6: Since S is to the East of R, we place S at (1, −1).Step 7: Now view S relative to Q. From Q at (0, 0) to S at (1, −1) the displacement is (1, −1), that is, 1 unit East and 1 unit South.Step 8: A movement combining East and South corresponds to the South-East direction.
Verification / Alternative check:We can also reason qualitatively without coordinates. Since R is South of Q, draw R below Q. Because S is East of R, draw S to the right of R. This places S diagonally below and to the right of Q, which is exactly South-East of Q. Thus, either with coordinates or a diagram, the outcome is the same.
Why Other Options Are Wrong:South-West would place S below and to the left of Q, which is inconsistent because S was placed to the right (East) of R and R is already South of Q. North-East would be above and to the right of Q, but S lies below Q. North-West would be above and to the left, again contradicting the description. The option "East" alone would ignore the fact that S is also South of Q.
Common Pitfalls:Students sometimes read P % Q + R - S as if it were an arithmetic expression and try to combine symbols algebraically. Instead, each pair must be interpreted as a separate directional relation. Another mistake is to reverse the direction, for example reading "A % B" as "B is East of A". Carefully noting which element is on the left of a symbol and which is on the right helps avoid this error.
Final Answer:In the expression P % Q + R - S, point S is located to the South-East of Q.

Question 19

Raman is performing yoga in a headstand position, with his head down and legs up, while his face is towards the West. In this inverted posture, in which cardinal direction will his left hand be pointing?

Accepted Answer

Introduction:This direction–sense problem involves an inverted body position. Raman is in a headstand with his head down, legs up, and face towards the West. We are asked to determine the direction of his left hand in this upside-down posture. The twist is that inversion reverses left and right relative to the ground, even though his face continues to point in the same direction.
Given Data / Assumptions:• Raman is doing yoga with his head down and legs up (a headstand).• His face is oriented towards the West throughout.• He is upside down relative to a normal standing position.• We assume his body has rotated only enough to invert head and feet, keeping his face still towards West.
Concept / Approach:When a person is standing upright facing West, the North lies on their right, and the South lies on their left. However, in a headstand where the body is inverted but still facing the same horizontal direction (West), the spatial orientation of left and right flips with respect to the ground. Intuitively, what was originally the person's left side now lies where the right side used to be when seen from the outside. Formalising this with a mental rotation clarifies that the left hand now points towards the North.
Step-by-Step Solution:Step 1: Consider Raman standing upright facing West. In that normal posture, North is to his right and South is to his left.Step 2: In the upright position facing West, his left hand points towards the South and his right hand towards the North.Step 3: Now invert him so that he is in a headstand but still facing West. This is equivalent to rotating his body 180 degrees around a horizontal axis running from front to back.Step 4: Under such a rotation, the direction of his face (towards West) remains the same, but his "up" direction reverses and the positions of his left and right sides swap relative to the ground.Step 5: As a result, the arm that is anatomically his left arm now points where his right arm was pointing when he was upright.Step 6: Earlier, his right arm pointed towards the North while facing West upright. Now, upside down, his left arm takes that place and therefore points towards the North.
Verification / Alternative check:You can verify this by imagining someone facing West and marking their hands: draw a figure facing left on paper (left representing West). Label the lower hand as left and the upper hand as right. Then rotate the page 180 degrees to represent a headstand: the face still points left (West), but the labels of the hands swap sides relative to the page edges. The hand that remains anatomically "left" is now on the side that was originally "right", pointing towards North.
Why Other Options Are Wrong:East and West correspond to the forward and backward directions relative to his face, and a side hand cannot point along the forward-facing direction when the arms are stretched out sideways. South would be the direction of his left hand in the upright position, but inversion reverses this. North-East is a diagonal that would require an upward component not described in the problem. Only North is consistent with the inversion of left and right when the face remains towards West.
Common Pitfalls:Many learners mistakenly assume that inversion does not affect left and right, or they try to imagine turning around vertically instead of flipping over horizontally. Others confuse the directions of the Sun or try to bring in shadow logic, which is not relevant here. A careful visualisation of an upside-down person or a simple sketch rotated by 180 degrees helps significantly.
Final Answer:In the described headstand posture, Raman's left hand will point towards the North direction.

Question 20

P started from his house walking towards the West. After walking 25 m, he turned right and walked 10 m, then turned right again and walked 15 m. After this, he has to turn right through an angle of 135 degrees and walk 30 m. In which direction shoul…

Accepted Answer

Introduction:This question combines straightforward direction movements with a slightly unusual turn of 135 degrees. P moves West initially, then makes two right-angle turns, and finally is asked to turn right through 135 degrees before walking further. We must determine the resulting direction of travel for this last segment.
Given Data / Assumptions:• P starts from his house walking towards the West.• He walks 25 m, turns right and walks 10 m.• He turns right again and walks 15 m.• After that, he is to turn right through 135 degrees and walk 30 m.• We are asked only for the direction of this last leg, not his exact coordinates.
Concept / Approach:The critical part is to track P's current facing direction before the 135 degree turn. Right and left turns are taken relative to the person's current direction. After determining that direction, we then imagine a 135 degree right turn, which corresponds to three 45 degree steps or one and a half right angles. On the compass, moving 135 degrees right from a given cardinal direction will land us on one of the diagonal directions (like South-West or South-East).
Step-by-Step Solution:Step 1: Initially, P faces West and walks 25 m. His facing direction remains West.Step 2: He turns right from West. On a compass, right from West points North. He walks 10 m North and is now facing North.Step 3: He then turns right again from North, which points East. He walks 15 m East and is now facing East.Step 4: Now he must make a right turn of 135 degrees from East. A 90 degree right turn from East would take him to South. An additional 45 degrees right from South leads to South-West.Step 5: Therefore, a single 135 degree right turn from East results in the direction South-West.Step 6: Thus, on his last leg, P should go in the South-West direction.
Verification / Alternative check:Think of the circle of directions: East → South-East (45 degrees) → South (90 degrees) → South-West (135 degrees) → West (180 degrees). Starting from East and turning right (clockwise) by 135 degrees takes you three steps to South-West. This matches our earlier breakdown of a 90 degree plus an additional 45 degree right turn.
Why Other Options Are Wrong:West would correspond to a 180 degree right turn from East, which is not what is specified. South would correspond to only a 90 degree right turn. South-East would result from only a 45 degree right turn. North-West is on the opposite diagonal and would require a different rotation (for example, 135 degrees left from East, not right). Only South-West matches exactly a 135 degree right turn from East.
Common Pitfalls:Many students misread "right at 135 degrees" as "right, then 135 degrees more", or confuse 135 degrees with 45 degrees. Some also forget to update P's facing direction after the earlier two right turns and assume he is still facing West. A good method is to draw a small compass, mark the current facing direction, and count 45 degree steps in the correct direction to reach the final orientation.
Final Answer:On the last leg, after turning right through 135 degrees, P should walk towards the South-West direction.

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