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Direction & Distance

Reasoning Ability · Core Logical Tools

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Overview

Direction questions track turns and distances on a compass; the final distance often uses Pythagoras.

Key points

Right turn from north faces east; left turn from north faces west.
Net displacement: add moves along the same axis, subtract opposite moves.
Shortest distance = √(net east–west² + net north–south²).
Shadows: in the morning the Sun is in the east, so shadows fall to the west; in the evening they fall to the east.
NE, NW, SE, SW lie midway between the main directions.

Explanation

Write the net displacement as (x, y) with east and north positive.
For "which direction from the start", read the signs of x and y.
Turns of 45° move to the in-between directions.
A full clockwise turn is 360°; three right turns equal one left turn.

Step by step

Draw moves.
Compute net displacement.
Find distance and direction.

Examples

Walk 3 km north and 4 km east: distance from the start = √(9 + 16) = 5 km, towards the north-east.
Facing north, turn right, right again, then left → you face east.
In the morning a man’s shadow falls to his right → he is facing south.

Traps and advanced points

Trap: Adding distances instead of using net displacement.
Trap: Confusing left and right after several turns.
Trap: Forgetting the direction of shadows.

Quick revision

Track (x, y).
Pythagoras for the final distance.
Morning shadow falls west.

Practice MCQs

A person walks 52 km east, 8 km north, then 46 km west. How far is the person from the start?
1. 12 km
2. 8 km
3. 10 km
4. 14 km
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Answer: (c) 10 km. Net movement: 6 km east and 8 km north.
A person walks 63 km east, 15 km north, then 55 km west. How far is the person from the start?
1. 15 km
2. 21 km
3. 19 km
4. 17 km
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Answer: (d) 17 km. Net movement: 8 km east and 15 km north.
A person walks 72 km east, 8 km north, then 66 km west. How far is the person from the start?
1. 12 km
2. 10 km
3. 14 km
4. 8 km
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Answer: (b) 10 km. Net movement: 6 km east and 8 km north.
A person walks 83 km east, 15 km north, then 75 km west. How far is the person from the start?
1. 19 km
2. 15 km
3. 21 km
4. 17 km
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Answer: (d) 17 km. Net movement: 8 km east and 15 km north.
A person walks 94 km east, 12 km north, then 89 km west. How far is the person from the start?
1. 11 km
2. 17 km
3. 13 km
4. 15 km
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Answer: (c) 13 km. Net movement: 5 km east and 12 km north.
A person faces East, walks 98 m straight, then turns right, then left, then right, then right, then right. Final facing direction?
1. East
2. South
3. North
4. West
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Answer: (c) North. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces North, walks 45 m straight, then turns left, then left, then left, then right, then left. Final facing direction?
1. South
2. West
3. East
4. North
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Answer: (c) East. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces North, walks 89 m straight, then turns left, then left, then right, then left, then right. Final facing direction?
1. North
2. South
3. West
4. East
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Answer: (c) West. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces South, walks 35 m straight, then turns left, then right, then right, then right, then right. Final facing direction?
1. South
2. North
3. West
4. East
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Answer: (d) East. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces South, walks 75 m straight, then turns left, then right, then right, then left, then left. Final facing direction?
1. South
2. East
3. West
4. North
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Answer: (b) East. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person walks 12 km east, 8 km north, then 6 km west. How far is the person from the start?
1. 8 km
2. 14 km
3. 12 km
4. 10 km
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Answer: (d) 10 km. Net movement: 6 km east and 8 km north.
A person faces West, walks 56 m straight, then turns right, then right, then left, then left, then right. Final facing direction?
1. North
2. West
3. South
4. East
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Answer: (a) North. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces South, walks 83 m straight, then turns left, then right, then right, then right, then left. Final facing direction?
1. West
2. East
3. South
4. North
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Answer: (a) West. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces East, walks 42 m straight, then turns right, then left, then right, then left, then left. Final facing direction?
1. East
2. South
3. West
4. North
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Answer: (d) North. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person walks 19 km east, 4 km north, then 16 km west. How far is the person from the start?
1. 9 km
2. 3 km
3. 5 km
4. 7 km
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Answer: (c) 5 km. Net movement: 3 km east and 4 km north.