Direction and Distance

Why This Chapter Matters

Direction questions have 3-5 marks in banking exams. Shadow-based problems and displacement calculations are trickier. Build a strong compass and always draw the path.

Core Concepts

1. Compass Directions

        North
          |
West -----+-----East
          |
        South

Left turn from North → West (anti-clockwise)

Right turn from North → East (clockwise)

Intercardinal: NE, NW, SE, SW (45° between cardinal points)

2. Shadow Problems

Morning (sunrise in East):

Shadow falls to the WEST of object.

If person faces North, shadow is to their LEFT (West).

If person faces East, shadow is BEHIND them (West).

Evening (sunset in West):

Shadow falls to the EAST of object.

If person faces North, shadow is to their RIGHT (East).

At noon: Shadow falls to the NORTH (in India, which is in the Northern hemisphere).

3. Displacement vs Distance

Distance = total path length (sum of all segments)

Displacement = straight-line distance from start to end

For perpendicular turns: displacement = √(a² + b²) using Pythagoras

4. Approach to Solving

Step 1: Draw the path on paper.

Step 2: Mark start point. Draw each move with arrow.

Step 3: For displacement, find net horizontal and vertical movement.

Step 4: Apply Pythagoras if needed.

5. After Multiple Turns — Net Direction

Track cumulative direction:

Start facing North → Turn Left → Now facing West

Turn Right → Now facing North again

Turn 180° → Now facing South

Solved Examples

Q1: Starting from home, John walks 4 km North, then 3 km East, then 4 km South. How far is he from home?

Net North-South: +4 - 4 = 0 (back to same latitude).

Net East-West: +3 East.

Displacement = 3 km East.

Q2: A person walks 10 km South, then turns left and walks 6 km, then turns left and walks 10 km. Final displacement?

South 10 → turn left (East) 6 → turn left (North) 10.

Net N-S: -10 + 10 = 0. Net E-W: +6. Displacement = 6 km East.

Q3: At 8 AM, A is standing facing North. His shadow falls to which side?

Morning sun in East → shadow to West.

Shadow falls to his LEFT (since he faces North, West is his left).

Previous Year Questions

SBI Clerk 2023: A walks 5 km East, 3 km North, 5 km West. Displacement from start?

Net E-W: 5-5=0. Net N-S: 3 North. Displacement = 3 km North.

IBPS PO 2022: Complex path with 4-5 turns. Find direction of starting point from ending point.

[Draw all moves, find final position relative to start, then describe direction]

Revision Notes

COMPASS:
N→turn left→W→turn left→S→turn left→E→turn left→N (anti-clockwise)
N→turn right→E→turn right→S→turn right→W→turn right→N (clockwise)

SHADOW:
Morning (sun in East): shadow → West
Evening (sun in West): shadow → East
Noon: shadow → North (in India)

DISPLACEMENT vs DISTANCE:
Distance = sum of all segments
Displacement = shortest path (Pythagoras for perpendicular moves)
= √(Horizontal² + Vertical²)

APPROACH: Always draw the path. Never solve mentally.