SSC & BANK EXAMS: REASONING · DIRECTION SENSE

Direction sense: distance and direction

Track the position on a grid (East = +x, North = +y). Add up the x and y movements, then distance = √(x² + y²).

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Worked examples

Example 1 · level 1

Kabir starts from the cricket ground and walks 15 km towards the West, then turns right and walks 8 km. How far and in which direction is Kabir now from the starting point?

19 km North-West
23 km North-West
17 km South-East
17 km North-West

Show solution

Positions after each walk: (-15, 0) → (-15, 8).
Net: 15 km West, 8 km North.
Distance = √(225 + 64) = 17 km.
Answer: 17 km North-West.

Answer: 17 km North-West

Example 2 · level 2

Isha starts from the railway station and walks 3 km towards the West, then turns left and walks 2 km, then turns left and walks 15 km, then turns left and walks 7 km. How far and in which direction is Isha now from the starting point?

13 km North-East
13 km South-East
17 km North-East
13 km South-West

Show solution

Positions after each walk: (-3, 0) → (-3, -2) → (12, -2) → (12, 5).
Net: 12 km East, 5 km North.
Distance = √(144 + 25) = 13 km.
Answer: 13 km North-East.

Answer: 13 km North-East

Example 3 · level 3

Ayaan starts from the cricket ground and walks 5 km towards the West, then turns right and walks 3 km, then turns left and walks 8 km, then turns right and walks 5 km, then turns right and walks 7 km. How far and in which direction is Ayaan now from the starting point?

14 km North-West
12 km North-West
10 km South-East
10 km North-West

Show solution

Positions after each walk: (-5, 0) → (-5, 3) → (-13, 3) → (-13, 8) → (-6, 8).
Net: 6 km West, 8 km North.
Distance = √(36 + 64) = 10 km.
Answer: 10 km North-West.

Answer: 10 km North-West