find both direction & distance Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1

Amit starts from point A and walks 5 m towards North-East direction and reaches point B. From here, he travels 8 m in the East direction and reaches point C. From C, he travels towards South-West direction and reaches point D after travelling a distance equal to AB. At last, he turns towards the West direction and reaches point A. How much distance has been covered by Amit and which geometrical figure has been formed by the path travelled by him?

a) 16 m, parellelogram

b) 26 m, parellelogram

c) 26 m, square

d) 26 m, trapezium

Answer: (b)

According to the question, the direction diagram is as follows. 

Therefore, Required distance = AB + BC + CD + DA

= 5 + 8 + 5 + 8 = 26 m.

and the geometrical figure formed is Parallelogram.

Question : 2

Sanjay's school is 10 $√2$ km in North - West direction from his house. The officee of his father is 10 km in South direction from the school. The multiplex hall is 10 km towards East from the school. How far and in which direction is the multiplex hall from the office of his father?

a) $10√2$ km, north - East

b) 20 km, North - East

c) 10 km, South - East

d) $20√2$ km, north - East

e) Cannot be determined

Answer: (a)

According to the question, the direction diagram will be as follows.

As in a square, diagonals are equal. Therefore, SH = OM = 10√2 km

Therefore, Required distance, OM = Distance between office and multiplex = 10√2 km

Also, it is clear from diagram that multiplex (M) is to the North - East of O (office)

So, the multiplex is $10√2$ km North - East from office.

Question : 3

Pankaj travels 10 m in North direction, he turns right and travels 20 m. Again he turns towards right and travels 25 m. Then, he turns towards left and travels 15 m. In which direction and how far is Pankaj from his original position?

a) 35 m, East

b) 10 m, West

c) 25 m, East

d) 55 m, West

e) None of these

Answer: (e)

According to the question, the direction diagram will be as follows.

A = Starting point, E = Finishing point DE = 15 m,

BC = FD = 20 m FE = FD + DE = 20 + 15 = 35 m

AF = BF - AB = 25 - 10 = 15 m

Therefore, Required distance, AE = $√{(AF)^2 + (FE)^2}$

= $√((15)^2 + (35)^2)$

= $√{(225 + 1225)}$

= $√1450$

and the direction is South-East

Question : 4

Starting from a point, raju walked 12 ft North, he turned right and walked 10 ft, he again turned right and walked 12 ft, then the turned left and walked 5 ft. How far is he now and in which direction from the starting point?

a) 27 ft towards East

b) 5 ft towards East

c) 10 ft towards West

d) 15 ft towards East

e) 35 ft towards North

Answer: (d)

According to the questions, the direction diagram is as follows.

AB = CD = 12 ft

BC = AD = 10 ft

DE = 5 ft

Therefore, Required distance, AE = AD + DE = 10 + 5 = 15 ft

Hence at finishing point E, Raju is 15 ft East from starting point A.

Question : 5 [I.B.P.S. (PO) 2011]

A school bus driver starts from the school, drives 2 km towards North, takes a left turn and drives for 5 km. He, then takes a left turn and drives for 8 km before taking a left turn again and driving for further 5 km. The driver finally takes a left turn and drives 1 km before stopping. How far and towards which direction should the driver drive to reach the school again?

a) 3 km towards North

b) 7 km towards East

c) 6 km towards South

d) 6 km towards West

e) 5 km towards North

Answer: (e)

According to the question, the direction diagram will be as follows.

Now, BC = DE = 5 km, CD = BE = 8 km AB = 2 km, EF = 1 km

Therefore, Required distance, AF = BE - (AB + EF) = 8 - (2 + 1) = 8 - 3 = 5 km.

From the direction diagram, it is clear that the bus is present finally in the South direction of school.

So, the driver needs to drive 5 km towards North direction to reach the school.

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