Direction & distance
Direction sense questions — free, machine-verified practice
Direction sense questions describe a journey through turns and distances and ask for the final direction or the shortest distance back to the start. Draw the path with north fixed at the top of the page, total the movement north-south and east-west separately, and combine the two net legs with Pythagoras when a straight-line distance is asked.
Direction and distance carries two to three marks in banking prelims and appears reliably in SSC General Intelligence. It is the topic where drawing beats reasoning most decisively: candidates who sketch the path finish in under a minute, and those who track turns mentally get the direction right but the distance wrong.
How to solve direction sense questions by tracking net displacement
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Fix north at the top of the page and never rotate it
Draw the compass once in the corner and keep the page still. Rotating the paper to follow a turn is the fastest way to reverse east and west without noticing. The path bends; the compass does not.
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Turn relative to the direction of travel, not the page
A left turn while walking south takes you east, not west. Before applying any turn, note which way the walker is currently facing and rotate from there. This one habit removes most direction errors, because the trap is always a turn taken while facing south.
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Total the two axes separately
Add all northward distances and subtract all southward ones for the net vertical leg; do the same for east and west. Two numbers describe the whole journey no matter how many turns it contained, and intermediate positions stop mattering entirely.
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Use Pythagoras only for straight-line distance
The shortest distance from the start is the square root of the sum of the two net legs squared. Most exam questions are built on 3-4-5 or 6-8-10 triangles, so recognising those saves the arithmetic. If the question asks for distance walked rather than distance from the start, add the legs instead — they are different questions.
Where each turn takes you
Where each turn takes you
| Facing, then turning | New direction |
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| North, turn left | West |
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| North, turn right | East |
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| South, turn left | East |
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| South, turn right | West |
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| East, turn right | South |
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| West, turn right | North |
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Practise direction sense questions right now
Every question below was generated by the same engine that mints the Deduce daily puzzle, and machine-proven to have exactly one correct answer before it reached this page. The walkthrough is the engine's own, step for step.
Question 1
How far and in which direction is Arjun from the starting point?
Arjun starts from a point and walks 8 m towards South.
He then turns left and walks 13 m.
He then turns right and walks 5 m.
He then walks 4 m towards West.
He then walks 4 m towards North.
- 11√2 m South-East
- 9√2 m South-East
- 9 m South-East
- 9√2 m East
- 9√2 m South
Show the worked solution
- Take the start as (0, 0), with East as +x and North as +y.
- Step 1: walks 8 m towards South → (0, -8).
- Step 2: turns left (now facing East) and walks 13 m → (13, -8).
- Step 3: turns right (now facing South) and walks 5 m → (13, -13).
- Step 4: walks 4 m towards West → (9, -13).
- Step 5: walks 4 m towards North → (9, -9).
- Net position (9, -9) = 9 m East and 9 m South — equal components point exactly South-East, and the distance is 9√2 m.
- So Arjun is 9√2 m South-East of the starting point.
Question 2
In which direction is Anjali facing now?
Anjali starts from a point and walks 3 m towards West.
She then turns left and walks 5 m.
She then walks 5 m towards East.
She then turns right and walks 7 m.
She then turns right and walks 7 m.
- East
- West
- South
- North
- Cannot be determined
Show the worked solution
- Take the start as (0, 0), with East as +x and North as +y.
- Step 1: walks 3 m towards West → (-3, 0).
- Step 2: turns left (now facing South) and walks 5 m → (-3, -5).
- Step 3: walks 5 m towards East → (2, -5).
- Step 4: turns right (now facing South) and walks 7 m → (2, -12).
- Step 5: turns right (now facing West) and walks 7 m → (-5, -12).
- She faces the direction she last walked, and every turn is tracked above.
- So Anjali is now facing West.
Question 3
How far and in which direction is Anjali from the starting point?
Anjali starts from a point and walks 7 m towards East.
She then walks 13 m towards South.
She then turns right and walks 15 m.
She then turns right and walks 5 m.
- 8√2 m West
- 16 m South-West
- 10√2 m South-West
- 8√2 m North-East
- 8√2 m South-West
Show the worked solution
- Take the start as (0, 0), with East as +x and North as +y.
- Step 1: walks 7 m towards East → (7, 0).
- Step 2: walks 13 m towards South → (7, -13).
- Step 3: turns right (now facing West) and walks 15 m → (-8, -13).
- Step 4: turns right (now facing North) and walks 5 m → (-8, -8).
- Net position (-8, -8) = 8 m West and 8 m South — equal components point exactly South-West, and the distance is 8√2 m.
- So Anjali is 8√2 m South-West of the starting point.
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Common mistakes
Turning relative to the page while facing south
When the walker faces south, a left turn goes east — the opposite of what the page suggests. Every set contains at least one southward turn for exactly this reason. Note the facing direction before every turn.
Confusing distance walked with distance from the start
Total distance walked is the sum of every leg. Distance from the starting point is the straight line, found with Pythagoras. Both appear as options, so read which one the question wants before computing.
Ignoring the final facing direction
Questions often ask which direction the walker now faces, not where they are. These are different answers and the option list will contain both. Track facing separately from position throughout.
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FAQ
If I am facing south and turn left, which direction am I facing?
East. Turns are always relative to the direction you are currently facing, not to the page. Facing south, your left hand points east and your right points west — the reverse of the situation when facing north. This is the most common single error in the topic, and papers place a southward turn in nearly every set.
How do I find the shortest distance back to the starting point?
Net your north-south movement into one number and your east-west movement into another, then take the square root of the sum of their squares. If the net legs are 6 and 8, the shortest distance is 10. Exam questions overwhelmingly use 3-4-5 style triangles, so the arithmetic stays clean.
Do I need to draw the diagram, or can I track it mentally?
Draw it. The diagram takes about twenty seconds and eliminates the entire class of turn-direction errors. Candidates who track mentally usually get the final direction right and the distance wrong, because intermediate positions are hard to hold while turning.
What is the difference between direction sense and a shadow-based question?
Shadow questions add one fact: in the morning the sun is in the east so shadows fall west, and in the evening the reverse. Once that fixes the facing direction, the question becomes an ordinary direction-sense problem and the same net-displacement method applies.
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