The document provides examples and explanations for solving direction and distance problems. It begins by explaining how to draw basic direction maps and use the Pythagorean theorem to calculate distances. Multiple examples are then given of direction and distance word problems, showing the step-by-step workings to find the direction and distance from a starting point based on movements provided. Hints and explanations are provided for each example to help the reader understand the solutions.

1. Direction Sense
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2. Directions
Direction sense questions asked in the exam are based on two
concepts - Distance and Direction
You might be asked to calculate the distance or the direction.
The first thing that we have to learn is to draw basic direction
map.
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3. Pythagorean Theorem
In a right angled triangle, the square of the hypotenuse is
equal to the sum of the squares of the other two sides.
AB = a, BC= b, and CA= c
Angle B is 90 degrees
a2 + b2 = c2
Note: Triplets – 3,4,5; 5,12,13; and all other multiples of such triplets.
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4. Examples
A person starts from position A. He goes towards the east
and then takes a right turn. Again the person takes a left
turn and moves and then again he moves 45 degrees right.
In which direction he is from the starting position?
Answer: SE direction from the starting point.
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5. Examples
Y is in the East of X which is in the North of Z. If P is in
the South of Z, then in which direction of Y, is P?
Hint:
Answer: P is in South West of Y
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6. Examples
A man is facing north. He turns 45 degree in the clockwise
direction and then another 180 degree in the same direction
and then 45 degree in the anticlockwise direction and then
225 degrees clockwise. Find which direction he is facing
now ?
Answer: North East
Hint: +45+180-45+225= 405(360+45) = So, 45 clockwise
from the initial position
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7. Examples
A man is facing west. He turns 45 degree in the clockwise
direction and then another 180 degree in the same direction
and then 270 degree in the anticlockwise direction. Find
which direction he is facing now ?
a) South-West
b) West
c) South
d) East-South
Answer : South West
Hint: +45+180-270= -45, which implies 45 degrees
anticlockwise is net rotation
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8. Example
If South-East becomes North, North-East becomes West
and so on. What will West become?
Answer: West will become South East
Hint: As South East becomes North, Rotate the figure by
135 degrees anti clockwise and compare the new figure
with the original direction map.
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9. Examples
One evening, Raja started to walk toward the Sun. After walking a
while, he turned to his right and again to his right. After walking a
while, he again turned right. In which direction is he facing?
(SSC CGL 2011)
(a) South
(b) East
(c) West
(d) North
Answer: South
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10. Examples
One morning, Udai and Vishal were talking to each other
face to face at a crossing. If Vishal’s shadow was exactly to
the left of Udai, which direction was Udai facing?
Answer: North
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11. Examples
If I move 4 km towards east and then I travel 3 km towards
the north. What is my distance from the starting point?
Answer: 5 KM from the starting point.
Hint: 32
+ 42
= c2
=> c = 5
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12. Examples
Rohit walked 25 metres towards South. Then he turned to his
left and walked 20 metres. He then turned to his left and
walked 25 metres. He again turned to his right and walked 15
metres. At what distance is he from the starting point and in
which direction ?
a. 35 metre, North
b. 30 metre, South
c. 35 metre, East
d. 30 metre, North
Answer:
Rohit's distance from the starting point A will = 20 + 15 = 35
metre
And direction with reference to the starting point is east.
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13. Examples
From his house, Lokesh went 15 kms to the North. Then he
turned West and covered 10 kms. Then he turned South and
covered 5 kms. Finally, turning to East, he covered 10 kms.
How far and which direction is he from his house ?
Answer: North, 10 KM distance.
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14. Examples
Saurav walks 10 km towards North. From there he walks 6
Km towards South. Then, he walks 3 Km towards east.
How far and in which direction is he with reference to his
starting point ?
Answer: 5KM, North East
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15. Examples
Kiran walks 20 metres towards North. He then turns left
and walks 40 metres. He again turns left and walks 20
metres. Further, he moves 20 metres after turning to the
right. How far is he from his original position and which
direction is he facing?
Answer: 60m, West.
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16. Examples
One day, Raviraj left home and cycled 20 Km southwards,
turned right and cycled 10 km and turned right and cycled
20 Km and turned left and cycled 20 Km. How many
kilometres will he have to cycle to reach his home straight ?
a) 50 Km
b) 30 Km
c) 40 Km
d) 60 Km
Answer: 30KM
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17. Examples
A dog runs 20 metres towards East and turns Right, runs 10
metre and turns to right, runs 12 metres and again turns to left,
runs 5 metre and then turns to left, runs 12 metre. Now which
direction dog is facing and what distance is it from the starting
point?
Answer: East and 25 meters.
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18. Examples
A child is looking for his father. He went 90 metres in the East before turning to his right. He went 20
meters before turning to his right again to look for his father at his uncle’s place 30 metres from this
point. His father was not there. From here he went 100 metres to the North before meeting his father in
a street. What is the smallest distance between the starting point and his father’s position?
1. 80 metres
2. 100 metres
3. 140 metres
4. 260 metres
Answer: 100 meters
Hint: 602
+802
= c2
=> c=100
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19. Examples
B is 7 metres away in the north of A. A moves 9 metres towards east from the starting
point, takes a right turn and walks 2 metres, then takes a left turn and moves 1 metre
and finally he takes a left turn and moves 9 metres. Now, how far and in which
direction is A from the B? (SBI SO 2014)
(a) 5 metres, East
(b) 10 metres, West
(c) 5 metres, West
(d) 10 metres, East
(e) None of these
Answer: 10 meters, East
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