Q: Multi-turn route and facing direction: A man walks 4 miles north, left 6 miles, right 3 miles, right 4 miles (rest), then straight 2 miles, right 1 mile. In which direction is he finally facing?

Introduction / Context: This problem checks directional tracking after multiple moves and turns, including a pause that does not affect heading. Given Data / Assumptions: Start facing north by implication. Moves: N 4 → L (to west) 6 → R (to north) 3 → R (to east) 4 → rest → straight 2 (still east) → R (to south) 1. Asked: final facing direction (not location). Concept / Approach: Track headings explicitly after each turn. Rest pauses do not alter heading; “straight” means continue current heading. Step-by-Step Solution: Initial: face North, go 4.Left turn ⇒ face West, go 6.Right turn ⇒ face North, go 3.Right turn ⇒ face East, go 4. Rest.Straight 2 ⇒ still face East.Right turn ⇒ face South, go 1. Verification / Alternative check: Representing headings as N, W, N, E, E, S confirms the final orientation is South. Why Other Options Are Wrong: North/East/West conflict with the last right turn to south. South-east is a bearing, not a facing after a single orthogonal step. Common Pitfalls: Confusing “facing” with “position from start.” The question asks only the facing direction at the end. Final Answer: South

Q: Relative position from start after rectangular path: Arun: A→B 10 km East, B→C 3 km North, C→D 12 km West, D→E 3 km South. From the starting point A, in which direction is point E?

Introduction / Context: A standard grid-walk with cardinal legs. We must identify the final location relative to the origin (A). Given Data / Assumptions: A→B: +10 x. B→C: +3 y. C→D: −12 x. D→E: −3 y. Concept / Approach: Sum x and y displacements separately to get E’s coordinates relative to A. Step-by-Step Solution: Net x = +10 − 12 = −2 (2 km West).Net y = +3 − 3 = 0.Therefore, E is due West of A. Verification / Alternative check: Drawing a quick rectangle shows overshoot by 2 km to the west after returning south. Why Other Options Are Wrong: East/North/South would require nonzero x or y in those respective senses, which is not the case. Common Pitfalls: Losing track of signs during the west leg; keep axes consistent. Final Answer: West

Q: Facing direction after two right turns: A man walks 2 km north, turns right and walks 2 km, turns right again and continues. Which direction is he facing now?

Introduction / Context: This item is about orientation (heading) after successive right turns starting from north. Given Data / Assumptions: Initial heading: North. First right ⇒ East. Second right ⇒ South. Asked: current facing immediately after the second right while he proceeds. Concept / Approach: Turning right rotates the heading 90° clockwise each time. Two such turns from North lead to South. Step-by-Step Solution: North → (right) East → (right) South. Verification / Alternative check: Compass mnemonic (N→E→S→W clockwise) confirms the result. Why Other Options Are Wrong: East is the intermediate heading after the first right. North/West contradict the specified turns. Common Pitfalls: Confusing “direction facing” with “direction of displacement”—we need the immediate heading. Final Answer: South

Question 1

Rimpy walks south 15 m from home, then north 20 m, then east 10 m, then south 5 m. How far is she from home now, and in which direction relative to her starting point?

Accepted Answer

Introduction / Context: This problem asks for the resultant displacement after several orthogonal moves. You can track North–South and East–West components separately and combine them to get the final position. Given Data / Assumptions: South 15 m, then North 20 m, then East 10 m, then South 5 m. Take North and East as positive directions; South and West as negative. We need both distance and direction of the endpoint from start. Concept / Approach: Sum vertical components and horizontal components independently. The Pythagorean theorem is only needed if both components are nonzero. If one component sums to zero, the final displacement equals the magnitude of the other component alone. Step-by-Step Solution: Vertical: −15 + 20 − 5 = 0.Horizontal: +10 (East).Net position: exactly 10 m to the East of start. Verification / Alternative check: Draw a quick grid: the northward 20 cancels the two southward moves (15 and 5) perfectly, leaving only an eastward offset of 10 m. Why Other Options Are Wrong: South-East or North-East would require a nonzero vertical component. West contradicts the net East movement. Common Pitfalls: Incorrectly adding vertical moves or forgetting that the last southward 5 m completes the cancellation. Final Answer: 10 meters, East

Question 2

Rimpy walks 250 m North from home, turns right and travels 20 m East, then turns right again and goes 250 m South. How much distance must she still cover to return straight to her home?

Accepted Answer

Introduction / Context: This is a rectangular path with two equal and opposite long legs (250 m each) and one short side (20 m). After the described movements, you must compute the straight-line distance back to home. Given Data / Assumptions: North 250 m from home. Right turn → East 20 m. Right turn → South 250 m. Home is directly West from the endpoint by the short offset. Concept / Approach: The northward leg and the southward leg cancel. Only the 20 m eastward shift remains. The distance to go straight back home is the horizontal offset between the current position and the vertical line through home. Step-by-Step Solution: Vertical: +250 − 250 = 0 → same latitude as home.Horizontal: +20 (East) → 20 m to the East of home.So she must travel 20 m West to return. Verification / Alternative check: Sketch a rectangle: the path forms two parallel 250 m sides separated by 20 m. Why Other Options Are Wrong: 25 m, 4 m, or 40 m do not match the single horizontal offset produced by the path. Common Pitfalls: Treating the problem as a diagonal return; here the vertical part already cancels out fully. Final Answer: 20 m

Question 3

A school bus driver starts from the school, drives 2 km. towards North, takes a left turn and drives for 5 km. he then takes a left turn and drives for 8 km. before taking a left turn again and driving for further 5 km. The driver finally takes a le…

Accepted Answer

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Question 4

Town D lies 13 km East of town A. A bus starts at A, goes 8 km West, turns right and goes 5 km to reach B, then turns right again and travels 21 km to stop. How far and in which direction must it travel now to reach town D?

Accepted Answer

Introduction / Context: This path-tracking problem mixes absolute placements (D relative to A) with the bus’s movement segments. Converting the description into coordinates clarifies the final short leg required to reach D. Given Data / Assumptions: D is 13 km East of A. Segment 1: from A, 8 km West. Right turn from West → North; go 5 km to B. Right turn from North → East; go 21 km; stop. Concept / Approach: Use a coordinate frame with A at (0,0). Track each move and compare the final stop with D’s coordinate. The last required move is simply the vertical difference between the stop and D. Step-by-Step Solution: Let A = (0,0); D = (13,0).After 8 km West: (−8,0).Right to North, +5 km: (−8,5).Right to East, +21 km: (13,5).To reach D (13,0): move 5 km South. Verification / Alternative check: Plot the points: the final x matches D exactly (13); only y differs by +5. Why Other Options Are Wrong: 13 km South/21 km South: exaggerate the needed vertical correction. 5 km West: would change x, which already matches D. Common Pitfalls: Forgetting that a right turn from North leads to East; swapping axes signs. Final Answer: 5 Km. towards South

Question 5

Rajesh walks 4 km East from home, then turns right and walks 3 km South. What is his straight-line distance from home?

Accepted Answer

Introduction / Context: Two perpendicular moves form the legs of a right triangle. The shortest distance from start to end is the hypotenuse, computed by the Pythagorean theorem. Given Data / Assumptions: 4 km East, then 3 km South. We need straight-line distance from home to the endpoint. Concept / Approach: Right triangle with legs 4 and 3 has hypotenuse 5 (the well-known 3-4-5 triangle). Units remain in kilometres. Step-by-Step Solution: Let legs be a = 4, b = 3.Distance d = sqrt(a^2 + b^2) = sqrt(16 + 9) = sqrt(25) = 5. Verification / Alternative check: Memorized Pythagorean triples (3-4-5) quickly confirm the result without full calculation. Why Other Options Are Wrong: Values other than 5 contradict the Pythagorean relation for a right triangle with legs 3 and 4. Common Pitfalls: Mistaking 4.5 or 5.5 as plausible averages; the distance must satisfy a^2 + b^2 = d^2. Final Answer: 5 km.

Question 6

Ricky travels 5 km in a straight line from home (assume standard convention: initial heading North), then takes a right turn and goes 6 km, then takes a left turn and goes 3 km. What is his straight-line distance from home now?

Accepted Answer

Introduction / Context: The original statement does not specify the first direction. Under the standard recovery convention for such items, we assume the first leg is due North. After that, a right turn leads to East, and a subsequent left brings the heading back to North. We must compute the net displacement. Given Data / Assumptions: Assumed initial heading: North (5 km). Right turn → East (6 km). Left turn from East → North (3 km). Compute straight-line distance from home to the final point. Concept / Approach: Sum orthogonal components. North–South total: 5 + 3 = 8 km North. East–West total: 6 km East. Use the Pythagorean theorem for the resultant. Step-by-Step Solution: Vertical component: 8 km North.Horizontal component: 6 km East.Distance d = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10 km. Verification / Alternative check: The legs 6 and 8 form another well-known Pythagorean triple with hypotenuse 10. Why Other Options Are Wrong: 9, 11, or 12 km do not satisfy the relation d^2 = 6^2 + 8^2 for orthogonal movement. Common Pitfalls: Assuming a different initial heading without stating it; the Recovery-First Policy permits the standard North assumption when unspecified. Final Answer: 10 km

Question 7

Direction sense – “Pass the Ball” positions: A is 20 m north of B. B is 18 m east of C. C is 12 m west of A. If the ball was initially with B and is passed to C, from B’s starting point in which direction is C located?

Accepted Answer

Introduction / Context: This is a direction-sense puzzle about relative placement of three players A, B, and C on a plane. We must report the direction of C as seen from B’s original position at the moment the ball is passed from B to C. Given Data / Assumptions: A is 20 m north of B. B is 18 m east of C (so C is 18 m west of B). C is 12 m west of A (statement structure makes the set slightly inconsistent across all three constraints; we therefore rely on the minimally sufficient relation B–C for the query). Required: direction of C from B at the pass instant. Concept / Approach: Use a coordinate frame. Place B at the origin for convenience. Directions: east = +x, north = +y. If B is 18 m east of C, then C is 18 m to the west of B along the negative x-axis with no north/south displacement. Step-by-Step Solution: Let B = (0, 0).Given “B is 18 m east of C” ⇒ C = (−18, 0).Vector from B to C is (−18, 0) i.e., due West. Verification / Alternative check: Any north/south offset would have appeared as “north of” or “south of.” Absent such text, the direction must be purely horizontal towards the west. Why Other Options Are Wrong: North-West / South-West imply vertical displacement not stated. North or South contradicts the explicit east–west relation. South is unrelated to the described offset. Common Pitfalls: Trying to force all three relational lines into a single consistent triangle; the question only needs B→C direction, which is unambiguous. Final Answer: West

Question 8

Direction sense with two right turns: Gopal walks 2 km straight from his school, then turns right and walks 1 km, turns right again and walks 1 km to reach home. If his home lies south-east of the school, in which direction did he begin walking from…

Accepted Answer

Introduction / Context: The problem fixes the final relative bearing of home (south-east of school) and describes a 3-segment path with two consecutive right turns. We must infer the initial heading. Given Data / Assumptions: Segment 1: 2 km, unknown initial direction. Segment 2: 1 km after a right turn. Segment 3: 1 km after another right turn. Home is south-east of school (positive x, negative y relative to school). Concept / Approach: Two right turns advance the heading by 180° from the initial direction, and the two 1 km legs form perpendicular components. Test candidate initial headings and check the net displacement against “south-east.” Step-by-Step Solution: Assume initial East: displacement = (2, 0) + (0, −1) + (−1, 0) = (1, −1) ⇒ south-east ✔.Assume initial North: (0, 2) + (1, 0) + (0, −1) = (1, 1) ⇒ north-east ✖.Assume initial West or South produce other quadrants, not south-east. Verification / Alternative check: Only the “initial East” assumption yields a final vector with x > 0 and y < 0 (SE), matching the given relationship. Why Other Options Are Wrong: North/West/South beginnings land in different quadrants or axes. Common Pitfalls: Forgetting that the second and third segments are both 1 km; asymmetry would change the quadrant test. Final Answer: East

Question 9

Multi-turn route and facing direction: A man walks 4 miles north, left 6 miles, right 3 miles, right 4 miles (rest), then straight 2 miles, right 1 mile. In which direction is he finally facing?

Accepted Answer

Introduction / Context: This problem checks directional tracking after multiple moves and turns, including a pause that does not affect heading. Given Data / Assumptions: Start facing north by implication. Moves: N 4 → L (to west) 6 → R (to north) 3 → R (to east) 4 → rest → straight 2 (still east) → R (to south) 1. Asked: final facing direction (not location). Concept / Approach: Track headings explicitly after each turn. Rest pauses do not alter heading; “straight” means continue current heading. Step-by-Step Solution: Initial: face North, go 4.Left turn ⇒ face West, go 6.Right turn ⇒ face North, go 3.Right turn ⇒ face East, go 4. Rest.Straight 2 ⇒ still face East.Right turn ⇒ face South, go 1. Verification / Alternative check: Representing headings as N, W, N, E, E, S confirms the final orientation is South. Why Other Options Are Wrong: North/East/West conflict with the last right turn to south. South-east is a bearing, not a facing after a single orthogonal step. Common Pitfalls: Confusing “facing” with “position from start.” The question asks only the facing direction at the end. Final Answer: South

Question 10

Relative position from start after rectangular path: Arun: A→B 10 km East, B→C 3 km North, C→D 12 km West, D→E 3 km South. From the starting point A, in which direction is point E?

Accepted Answer

Introduction / Context: A standard grid-walk with cardinal legs. We must identify the final location relative to the origin (A). Given Data / Assumptions: A→B: +10 x. B→C: +3 y. C→D: −12 x. D→E: −3 y. Concept / Approach: Sum x and y displacements separately to get E’s coordinates relative to A. Step-by-Step Solution: Net x = +10 − 12 = −2 (2 km West).Net y = +3 − 3 = 0.Therefore, E is due West of A. Verification / Alternative check: Drawing a quick rectangle shows overshoot by 2 km to the west after returning south. Why Other Options Are Wrong: East/North/South would require nonzero x or y in those respective senses, which is not the case. Common Pitfalls: Losing track of signs during the west leg; keep axes consistent. Final Answer: West

Question 11

Facing direction after two right turns: A man walks 2 km north, turns right and walks 2 km, turns right again and continues. Which direction is he facing now?

Accepted Answer

Introduction / Context: This item is about orientation (heading) after successive right turns starting from north. Given Data / Assumptions: Initial heading: North. First right ⇒ East. Second right ⇒ South. Asked: current facing immediately after the second right while he proceeds. Concept / Approach: Turning right rotates the heading 90° clockwise each time. Two such turns from North lead to South. Step-by-Step Solution: North → (right) East → (right) South. Verification / Alternative check: Compass mnemonic (N→E→S→W clockwise) confirms the result. Why Other Options Are Wrong: East is the intermediate heading after the first right. North/West contradict the specified turns. Common Pitfalls: Confusing “direction facing” with “direction of displacement”—we need the immediate heading. Final Answer: South

Question 12

Rectangle loop and current heading: A walks 5 km north, left 3 km (west), then left 5 km (south). In which direction is he going now?

Accepted Answer

Introduction / Context: A compact orientation check after two left turns from an initial northbound path. Given Data / Assumptions: Start facing North, go 5 km. Left turn ⇒ West, go 3 km. Left turn ⇒ South, go 5 km. Concept / Approach: Each left turn is a 90° anticlockwise rotation of the heading. Track headings explicitly. Step-by-Step Solution: North → (left) West → (left) South. Verification / Alternative check: Visualising a U-shaped path confirms the final leg heads south. Why Other Options Are Wrong: North/East/West contradict the second left turn outcome. Common Pitfalls: Interpreting “direction going now” as a location question; it asks the present heading. Final Answer: South

Question 13

Four right-angle legs around a rectangle: Driver: North 20 km (breakfast) → Left 30 km (lunch) → Left 20 km (tea) → Left 30 km (to town). After evening tea, in which direction did he drive?

Accepted Answer

Introduction / Context: The itinerary forms a rectangle. We are asked the direction of the leg immediately after the “evening tea” stop (i.e., the third stop). Given Data / Assumptions: Leg 1: North 20 (breakfast). Leg 2: Left ⇒ West 30 (lunch). Leg 3: Left ⇒ South 20 (evening tea). Leg 4: Left from South ⇒ East 30 (to town). Concept / Approach: Left from South is East. The question references the leg after the evening tea stop, i.e., Leg 4. Step-by-Step Solution: Facing South at the tea stop → turn left → face East → drive 30 km. Verification / Alternative check: Opposite and adjacent legs of a rectangle match in length; the final leg mirrors the second. Why Other Options Are Wrong: North/West/South are inconsistent with a left turn from South. Common Pitfalls: Answering with the direction “to tea” (South) rather than “after tea” (East). Final Answer: East

Question 14

Grid of neighbors at 200 m diagonals: Rahim is at the origin. Babu: 200 m north-west; Joseph: 200 m south-west; Gopal: 200 m south-east of Joseph; Roy: 200 m north-east of Gopal. Where is Roy relative to Babu?

Accepted Answer

Introduction / Context: This is a composition of diagonal moves (NW, SW, SE, NE) on a square grid with equal step lengths (200 m). We compare Roy’s final coordinates to Babu’s coordinates. Given Data / Assumptions: Use unit steps for direction; distance equality preserves direction labels. Babu from Rahim: NW = (−1, +1). Joseph from Rahim: SW = (−1, −1). Gopal from Joseph: SE = (+1, −1). Roy from Gopal: NE = (+1, +1). Concept / Approach: Compute coordinates relative to Rahim, then subtract to get Roy relative to Babu. Step-by-Step Solution: Babu = (−1, +1).Joseph = (−1, −1).Gopal = (−1, −1) + (+1, −1) = (0, −2).Roy = (0, −2) + (+1, +1) = (1, −1).Roy − Babu = (1 − (−1), −1 − 1) = (2, −2) ⇒ South-East. Verification / Alternative check: Diagramming a 2×2 diamond centered near Rahim shows Roy diagonally opposite Babu along the SE diagonal. Why Other Options Are Wrong: South-west/North/North-east do not match the computed relative vector. Common Pitfalls: Mixing “relative to Rahim” with “relative to Babu.” Always subtract the reference point’s coordinates. Final Answer: South east

Question 15

Turn sequence from a westward start: A man starts walking West, then turns right, then right again, then left. Towards which direction is he walking now?

Accepted Answer

Introduction / Context: A concise orientation test with successive turns from an initial westward heading. Given Data / Assumptions: Start: West. Right turn ⇒ North. Right turn ⇒ East. Left turn ⇒ North. Concept / Approach: Update heading after each turn; distance is irrelevant for heading. Step-by-Step Solution: West → (R) North → (R) East → (L) North. Verification / Alternative check: Clockwise/anticlockwise compass cycle confirms final North. Why Other Options Are Wrong: East/West/South contradict the final left from East. Common Pitfalls: Over-tracking position; only the final heading is asked. Final Answer: North

Question 16

Position relative to start after a 6-leg walk: Child: 25 ft North → right 40 ft → right 45 ft → left 20 ft → left 20 ft → left 20 ft. Where is the child relative to the starting point?

Accepted Answer

Introduction / Context: We must find the final position relative to the origin after several orthogonal moves with alternating turns. Given Data / Assumptions: N 25 → E 40 → S 45 → E 20 → N 20 → W 20 (from North turning left). Asked: bearing of the final point from the start. Concept / Approach: Sum x and y components. Step-by-Step Solution: x: +40 + 20 − 20 = +40.y: +25 − 45 + 20 = 0.Net = (40, 0) ⇒ due East. Verification / Alternative check: Sketching quickly shows the path ends directly to the right of the start on the same horizontal line. Why Other Options Are Wrong: North/South/West imply nonzero y or negative x, which do not occur. Common Pitfalls: Mistaking the final left from North as “West then 20” (it is West indeed, already included in the x total). Final Answer: East

Question 17

Facing direction after two right turns: Seeta walks 2 km north, turns right 2 km, turns right again and proceeds. Which direction is she facing now?

Accepted Answer

Introduction / Context: Same structure as a typical two-right-turn problem starting from north; we need the current heading. Given Data / Assumptions: Start North → right → East → right → South. Concept / Approach: Two successive right turns rotate the heading by 180°. Step-by-Step Solution: North → East → South. Verification / Alternative check: Compass cycle confirms South. Why Other Options Are Wrong: They conflict with the rotation sequence. Common Pitfalls: Confusing facing direction with net displacement. Final Answer: South

Question 18

Return to origin with four right turns: Sanmitra: North 3 km → right 2 → right 5 → right 2 → right 2. Which direction is he facing now?

Accepted Answer

Introduction / Context: We track heading through four right turns; the path actually returns to the start before the final leg completes. Given Data / Assumptions: N 3 → E 2 → S 5 → W 2 → N 2. Asked: final facing after the last turn and walk. Concept / Approach: Each right rotates 90° clockwise. Track: N → E → S → W → N. Step-by-Step Solution: Final move is North; he is facing North. Verification / Alternative check: Coordinate sum returns to (0, 0); heading remains the last move’s direction, North. Why Other Options Are Wrong: They contradict the rotation sequence. Common Pitfalls: Assuming “return to start” implies facing the original heading automatically—here it happens to match, but compute turns explicitly. Final Answer: North

Question 19

Relative location from start after L-shaped detours: Ramesh: West 3 km → left 2 km → right 3 km → right 2 km. In which direction is he from his starting point now?

Accepted Answer

Introduction / Context: The question asks for Ramesh’s location relative to his starting point (not facing) after several orthogonal moves. Given Data / Assumptions: West 3, South 2 (left from West), West 3 (right from South), North 2 (right from West). Concept / Approach: Component-wise displacement. Step-by-Step Solution: x: −3 + (−3) = −6.y: −2 + 2 = 0.Net = (−6, 0) ⇒ due West of the start. Verification / Alternative check: Path symmetry shows the two 2 km vertical legs cancel. Why Other Options Are Wrong: They imply nonzero y or positive x which do not occur. Common Pitfalls: Answering with facing direction (North) instead of position; the prompt asks “in which direction is Ramesh from his starting point.” Final Answer: West

Question 20

Sequence of turns from a southward start: X walks southwards, then turns right, then left, then right. In which direction is he moving now?

Accepted Answer

Introduction / Context: Find the current heading after three turns from a southward start. Given Data / Assumptions: Start South. Right ⇒ West. Left ⇒ South. Right ⇒ West. Concept / Approach: Apply 90° rotations in order. Step-by-Step Solution: South → West → South → West. Verification / Alternative check: Compass rotation confirms the pattern. Why Other Options Are Wrong: They conflict with the final right from South. Common Pitfalls: Misreading left/right when facing South (swap errors). Final Answer: West

Direction Sense Test Questions