Direction Sense: Notes और MCQ Practice

आसान भाषा में

Direction Sense में हम distance, direction, speed और time को relative positions के हिसाब से समझते हैं। मानचित्र या diagram में North, South, East, West, NE, SW आदि को पहचानना और steps/turns को count करके final position निकालना hota hai.

Important Formulas / Rules

• Speed = Distance ÷ Time
• Distance = Speed × Time
• Time = Distance ÷ Speed
• Relative direction = Starting direction ± Turns (Right = +90°, Left = -90°)
• 1 km = 0.62 miles (approx.)

Quick Tricks

1. Clock Trick – 12 o’clock = North, 3 = East, 6 = South, 9 = West. Turn clockwise for right turns, anti‑clockwise for left.
2. Scale Shortcut – If map scale is 1 cm : 5 km, multiply measured cm by 5 to get distance in km.

Common Mistakes

• Ignoring opposite direction: South‑East को SE, not just E.
• Mixing up turn angles: 180° turn = U‑turn, not two 90° right turns (though result same, count correctly for questions asking number of turns).

Direction Sense (General Intelligence & Reasoning)

1. Concept

Direction sense deals with the ability to determine the relative position of objects, people or points with respect to each other. In exam questions you are usually given a starting point, a series of moves (turns, distances, angles) and you have to find the final direction or the direction of another object.

2. Important Formulas / Rules / Facts

• Basic directions: N, S, E, W and the four inter‑cardinal points NE, NW, SE, SW.
• Turning angles:
• Right turn = clockwise rotation.
• Left turn = anti‑clockwise rotation.
• Angle values:
• 90° = right angle (quarter turn).
• 180° = straight line (half turn).
• 45° = half of a right angle (used for NE, NW, SE, SW).
• Conversion between directions and angles:
• Starting from North, moving clockwise: N (0°), NE (45°), E (90°), SE (135°), S (180°), SW (225°), W (270°), NW (315°).
• Relative direction rule: If A faces X and turns right by 90°, A now faces the direction that is 90° clockwise from X.
• Clockwise/Anti‑clockwise rule for multiple turns: Add angles for clockwise turns, subtract for anti‑clockwise; keep the result within 0°‑360° by adding/subtracting 360° as needed.
• Finding direction between two points: Use the “North‑South” and “East‑West” components separately and combine them (e.g., if B is north and east of A, direction = NE).

3. Solved Examples

Example 1

Question: A person starts facing North. He turns right by 90°, walks 5 km, then turns left by 45° and walks another 3 km. What is his final facing direction?

Solution:

1. Start direction = N (0°).
2. Right turn 90° → direction = E (90°).
3. Left turn 45° → direction = 90° − 45° = 45° → NE.

Answer: North‑East (NE).

Example 2

Question: From point P, a person walks 10 km towards East, then turns left and walks 6 km, then turns left again and walks 10 km. What is the direction of the final point from P?

Solution:

1. First leg: East 10 km → position (10, 0).
2. Left turn from East = North. Walk 6 km → position (10, 6).
3. Left turn from North = West. Walk 10 km → position (0, 6).
4. Relative to P (origin), the final point is 0 km East‑West and 6 km North → direction = North.

Answer: North.

Example 3

Question: A man faces South. He turns right by 135° and walks 8 km. What is his new facing direction?

Solution:

1. South = 180°.
2. Right turn 135° → 180° + 135° = 315°.
3. 315° corresponds to North‑West (NW).

Answer: North‑West (NW).

Example 4

Question: A person starts at point X facing East. He makes the following moves: turn left 90°, walk 5 km; turn right 45°, walk 7 km; turn left 135°, walk 2 km. Find the direction of the final point from X.

Solution:

1. Start East (90°).
2. Left 90° → direction = North (0°). Position after 5 km: (0, 5).
3. Right 45° → direction = 0° + 45° = 45° (NE). Move 7 km: Δx = 7 × cos45° = 7 × 0.707 ≈ 4.95, Δy = 7 × sin45° ≈ 4.95. New position ≈ (4.95, 9.95).
4. Left 135° → direction = 45° − 135° = -90° → add 360° → 270° (West). Walk 2 km West: Δx = –2, Δy = 0. Final position ≈ (2.95, 9.95).
5. Relative to X, both x and y are positive → direction is North‑East (NE).

Answer: North‑East (NE).

Example 5

Question: A boy faces West. He turns right by 180° and walks 12 km. What direction is he now facing?

Solution:

1. West = 270°.
2. Right turn 180° → 270° + 180° = 450°. Subtract 360° → 90°.
3. 90° = East.

Answer: East.

4. Shortcuts and Tricks

• Clock‑face method: Visualise a clock; each hour = 30°. A right turn of 90° = 3 hours clockwise, left turn of 45° = 1½ hours anticlockwise.
• Use “+ for right, – for left” on a 0‑360° scale; keep a running total.
• Remember the 8 principal directions only. Any angle that is a multiple of 45° maps directly to one of them.
• When distance is irrelevant (only direction asked), ignore the length and track only the turning angles.
• Combine opposite moves: If you move East 10 km and later West 10 km, they cancel out – useful for quick elimination.

5. Common Mistakes to Avoid

• Confusing left and right turns after a previous turn; always refer to the current facing direction.
• Mixing up clockwise and anticlockwise signs; adopt a consistent rule (e.g., clockwise = +, anticlockwise = –).
• Forgetting to normalize angles within 0°‑360°; a result like 405° should be reduced to 45°.
• Ignoring the starting direction when the question states “facing South” etc.; many errors arise from assuming North as default.
• Treating 135° as a right turn only – it can be either right 135° or left 225°, both lead to the same final direction but the sign matters in calculations.