## Results

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### #1. A man walks 1 km to East and then he turns to South and walks 5 km. Again he turns to East and walks 2 km. After this he turns to North and walks 9 km. Now, how far is he from his starting point?

Solution:

Man’s Movement :

The last position of the man is P and OEP is a Right angled triangle in which
EP = 3 km and OE = 4 km
Thus,
OP = √(32  42)
OP = √25
OP = 5 km.

### #2. I walk 30 metres in North-West direction from my house and then 30 metres in South-west direction. After this I walk 30 metres in South-East direction. Now, I turn to my house, in what direction am I going?

Solution:

Movements are as follows:

Now, I am going in North-East Direction.

### #3. A man faces towards north. Turning to his right, he walks 25 metes. He then turns to his left and walks 30 metres. Next, he moves 25 metres to his right. He then turns to his right again and walks 55 metres. Finally, he turns to the right and moves 40 metres. In which direction is he from his starting point ?

Solution:

Man’s Movement :

Finally he is towards the South-East from his starting Point.

### #4. If South-East becomes North and South becomes North-East and all the rest directions are changed in the same manner, the what will be the direction for West ?

Solution:

If South-east becomes North and North East becomes West, therefore, the whole figure moves through 1350. Hence, West will be South-East.

See, Actual figure is rotating 1350 anticlockwise. So, When West will be rotated by same degree anticlockwise. It will hold the place of south-East.

### #5. If Rahim moves 20 metres in East direction and then turns to his left and then moves 15 metres and then he turns to his right and moves 25 metres. After this he turns to his right and moves 15 metres. Now, how far is he from starting point ?

Solution:

Rahim’s Movement

Therefore, the distance of Rahim from his starting point,
= 20 25
= 45 metres

### #6. Mohan was facing east. he walked 4 km forward and then after turning to his right walked 3 km.Again he turned to his right and walked 4 km. After this he turned back. Which direction was he facing at that time?

Solution:

Mohan’s Movement :

If Mohan turned back from final position he must be facing in the direction of East.

### #7. A cyclist goes 30 km to North and then turning to East he goes 40 km. Again he turns to his right and goes 20 km. After this he turns to his right and goes 40 km. How far is from his starting point ?

Solution:

Cyclist’s Movement :
Distance of the Cyclist from his starting Point O to end point D = 30-20 = 10 km

### #8. A direction pole was situated on the crossing. Due to an accident the pole turned in such a manner that the pointer which was showing East, started showing South. One traveler went to wrong direction thinking to be West. In what direction actually he was traveling?

Solution:
As East becomes South, therefore, the pole has turned through 900 in anticlockwise direction. hence, the West will be North.