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

Question : 21 [M.B.A. 1998]

Kunal walks 10 kilometres towards North. From there, he walks 6 kilometres towards South. Then, he walks 3 kilometres towards East. How far and in which direction is he with reference to his starting point?

a) 5 kilometres West

b) 5 kilometres North - East

c) 7 kilometres East

d) 7 Kilometres West

Answer: (b)

The movements of Kunal are as shown in Fig. 9

(A to B, B to C and C to D).

AC = (AB - BC) = (10 - 6) km = 4 km.

Clearly, D is to the North - east of A.

Therefore, Kunal's distance from statrting point A = AD = $√{AC^2 + CD^2}$ = $√{42 + 32}$ = $√25$ = 5 km.

So, Kunal is 5 km to the North - east of his statrting point.

Question : 22 [Asstt. Manager Exam, 2005]

Manick walked 40 metres towards North, took a left turn and walked 20 metres. He again took a left turn and walked 40 metres. How far and in which direction is he from the starting point?

a) 20 metres East

b) 20 metres North

c) 20 metres South

d) 100 metres South

e) None of these

Answer: (e)

The movements of Manick are as shown in Fig. 11

(A to B, B to C and C to D).

Clearly, ABCD is a rectangle and so AD = BC = 20 m.

Thus, D is 20 m to the west of A.

Question : 23 [A.T.M.A. 2004]

A villager went to meet his uncle in another village situated 5 km away in the North - east direction of his own village. From there he came to meet his father-in-law living in a village situated 4 km in the south of his uncle's village. How far away and in which direction is he now?

a) 3 km in the North

b) 3 km in the East

c) 4 km in the East

d) 4 km in the West

Answer: (b)

The villager moves from his village at O to his uncle's village at A and therafter to his father-in-law's village at B. (Fig. 19)

Clearly, ΔOBA is right - angled at B.

So, $OA^2 = OB^2 + AB^2$

$OB^2 = OA^2 - AB^2$

OB = $√{25 - 16}$ km = $√9$ km = 3 km.

Thus, B is 3 km to the east of his initial position O.

Question : 24 [M.A.T. 2004]

Sanjeev walks 10 metres towards the South. Turning to the left, he walks 20 metres and then moves to his right. After moving a distance of 20 metres, he turns to the right and walks 20 metres. Finally, he turns to the right and moves a distance of 10 metres. How far and in which direction is he from the starting point?

a) 10 metres North

b) 20 metres South

c) 20 metres North

d) 10 metres South

e) None of these

Answer: (b)

The movements of Sanjeev from A to F are as shown in Fig. 22.

Clearly, Sanjeev's distance from starting point A = AF = (AB + BF)

= AB + (BE - EF)

= AB + (CD - EF)

= [10 + (20 - 10)] m

= (10 + 10) m = 20 m.

Also, F lies to the south of A. So, Sanjeev is 20 metres to the south of his starting point.

Question : 25

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 metres East

b) 40 metres East

c) 35 metres North

d) 60 metres East

e) None of these

Answer: (a)

The movements of Rohit are as shown in Fig. 26.

Therefore, Rohit's distance from starting point A = AE = (AD + DE)

= (BC + DE) = (20 + 15) m = 35 m.

Also, E is to the East of A.

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