# Distance and direction calculation suitable for any competitive exam in India

Q1. From her house, Kimi went 15 km to the North. Then, she turned West and covered 10 km. Then, she turned south and covered 5 km. Finally turning to East, she covered 10 km. In which direction is she from her house?
A.East
B.West
C.North
D.South

Movements of Kimi are shown in the given figure.

Clearly, final position is T which is in the north of her house.

Q2. From his house, Deepak went 25 km to North then, he turned west and covered 15 km. Then, turned south and covered 10 km. Finally, turning to East, he covered 15 km. In which direction is he from his house?
A.North
B.South
C.West
D.East

Show the figure,

Starting from the point A and passing through the points B, C and D, Deepak reaches the point E. Hence, he is in North direction from his house.

Q3. Shyam goes to 5 km in the north from his school. Now, turning to the left, he goes to 10 km and again turn to left and goes to 5 km. How far he is from his school and which direction?
A.10 km, South from school
B.10 km, North from school
C.10 km, West from school
D.10 km, East from school

Let point A is the starting point I.e., school of Shyam

Point D is the ending point,
From, figure, AB = CD = 5 km
And AD = BC = 10 km
So, Shyam is 10 km far away from his school and in West direction from school.

Q4. A direction pole was situated on the road crossing. Due to an accident, the pole turned in such a manner that the pointer which was showing East, started showing South. Sita, a traveller went to the wrong direction thinking it to be west. In what direction actually she was travelling?
A.North
B.West
C.East
D.South

The pointer which was showing last started showing South.
After accident, E – S and S – W
W – N and N – E
So, Pointer turned 90 degree clockwise.

Q5. A and B start walking in opposite directions. A covers 3 km and B covers 4 km. Then, a turns right and walks 4 km while B turns left and walks 3 km. How far is each from the starting point?
A.10 km
B.8 km
C.5 km
D.4 km

Let A and B started from point O. A towards West and B towards East and at last they reached N and Q. Respectively,
ON = √[(NM)²+ (MO)²] ON = √(4²+ 3²)
ON = 5 km
And,
OQ = √[(NQ)²+ (NO)²] OQ = √(3²+ 4²)
OQ = 5 km

Q6. A man walks 6 km south, turns left and walks 4 km, again turns left and walks 5 km. Which direction is he facing now?
A.South
B.North
C.East
D.West

Let the man starts from the point A and passing through,
B and C, he reaches D. Clearly, he is now facing North.

Q7. Ram cycled 10 km southward from his home, turned right and cycled 6 km, turned right and cycled 10 km, turned left and cycled 15 km. How many kilometres will he have cycled to reach straight home?
A.10 km
B.21 km
C.16 km
D.20 km

Figure is drawn as,

Now, to go back home Ram has to cycle = ( ED + DA ) = (15 + 6) = 21 km

Q8. One day, Ravi left home and cycled 10 km southwards, turned right and cycled 5 km and turned right and cycled 10 km and turned left and cycled 10 km. How many kilometres will he now have to cycle in a straight line to reach his home?
A.10 km
B.15 km
C.20 km
D.25 km

Now, distance Ravi to cycle to reach home is (ED + DA) = (10 + 5) = 15 km

Q9. A man travels 4 km towards North, then travels 6 km towards East and further travels 4 km towards North. How far he is from the starting point?
A. 6 km
B. 14 km
C. 8 km
D. 10 km

Distance between the starting point and end point is AD.
Now, AD² = AE² + DE²
AD = √100 = 10 km

Q10. 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 anti-clockwise direction. Which direction is he facing now?
A.South
B.North – West
C.West
D.South – West

The movement of man is shown in the figure below

From figure, finally, he is facing in the OS direction, which is South West.

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