find distance only Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11

A boy rode his bicycle northwards, then turned left and rode one km and again turned left and rode 2 km. He found himself exactly one km west of his starting point. How far did he ride northwards initially?

a) 1 km

b) 2 km

c) 5 km

d) 8 km

e) 10 km

Answer: (b)

Clearly, the boy rode from A to B, then to C and finally up to D.

Since D lies to the west of A, so required distance = AB = CD = 2 km.

Question : 12 [M.A.T. 2005]

A man leaves for his office from his house. He walks towards East. After moving a distance of 20 m, he turns South and walks 10 m. Then he walks 35 m towards the West and further 5 m towards the North. He then turns towards East and walks 15 m. What is the straight distance (in metres) between his initial and final positions?

a) 0

b) 5

c) 15

d) Cannot be determined

e) None of these

Answer: (b)

The movements of the man from A to F are as shown in Fig. 13

Clearly, DC = AB + EF. Therefore, F in line with A.

Also, AF = (BC - DE) = 5 m.

So, the man is 5 metres away from his initial position.

Question : 13

A man walks 30 metres towards South. Then, turning to his right, he walks 30 metres. Then, turning to his left, he walks 20 metres. Again, he turns to his left and walks 30 metres. How far is he from his initial position?

a) 20 metres

b) 30 metres

c) 50 metres

d) 60 metres

e) 80 metres

Answer: (c)

The movements of the man are as shown in Fig. 25.

Therefore, Man's distance from initial position A.

= AE = (AB + BE) = (AB + CD)

= (30 + 20) m = 50 m.

Question : 14

Raj travelled from a point X straight to Y at a distance of 80 metres. He turned right and walked 50 metres, then again turned right and walked 70 metres. Finally, he turned right and walked 50 metres. How far is he from the starting point?

a) 10 metres

b) 20 metres

c) 50 metres

d) 70 metres

e) 90 metres

Answer: (a)

The movements of Raj are as shown in Fig . 30.

(X to Y, Y to A, A to B, B to C).

Therefore, Raj's distance from the starting point = XC = (XY - YC)

= (XY - BA)

= (80 - 70) m = 10 m.

Question : 15

Two houses start from the opposite points of a main road, 150 km apart. The first bus runs for 25 km and takes a right turn and then runs for 14 km. It then turns left and runs for another 25 km and takes the direction back to reach the main road. In the meantime, due to a minor breakdown, the other bus has run only 35 km along the main road. What would be the distance between the two buses at this point?

a) 65 km

b) 75 km

c) 80 km

d) 85 km

e) 90 km

Answer: (a)

Let X and Y be two buses. Bus X travels along the path PA, AB, BC, CD

Now, AD = BC = 25 km. So, PD = PA + AD = 50 km. Bus Y travels 35 km up to E.

Therefore, Distance between two buses = PQ - (PD + QE)

= [150 - (50 + 35)] km = 65 km.

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