A car travels 15 km east, turns left and travels 10 km, turns left again and travels 15 km, then turns right and travels 5 km. How far and in which direction is it from the start ?
Answer: A
Correct answer: 15 km north
The turns give the sequence east, north, west, north. The 15 km east and 15 km west cancel, while the northward legs add.
\[10 + 5 = 15 \text{ km towards the north}\]
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One morning after sunrise, Vimal started to walk. During this walking he met Stephen who was coming from opposite direction. Vimal watch that the shadow of Stephen to the right of him (Vimal). To Which direction Vimal was facing?
Answer: C
Correct answer: South
In the morning the sun is in the east, so every shadow points west. Stephen’s shadow ran westward and fell to Vimal’s right, so west was on Vimal’s right hand, which puts him facing south.
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A man is facing north-west. He turns 90º in the clockwise direction, then 180º in the anticlockwise direction and then another 90º in the same direction. Which direction is he facing now?
Answer: C
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As shown in fig. the man initially faces in the direction OP. On moving 90º clockwise, he faces in the direction OX. On further moving 180º anticlockwise, he faces in the direction OY. Finally, on moving 90ºanticlockwise, he faces in the direction OZ, which is South-east.
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Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his original position ?
Answer: C
Correct answer: 60 metres
The northward and southward legs cancel - 20 north and then 20 south - leaving \( 40 + 20 = \mathbf{60} \) metres westward.
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If A x B means A is to the south of B; A + B means A is to the north of B; A % B means A is to the east of B; A - B means A is to the west of B; then in P % Q + R - S, S is in which direction with respect to Q ?
Answer: A
Correct answer: South-East
Take the relations in the order they are written. \( P \% Q \) fixes P east of Q. \( Q + R \) fixes Q north of R, so R is displaced south from Q. \( R - S \) fixes R west of S, so S is displaced east from R. S is therefore both south and east of Q - south-east. The first relation involving P is not needed for this question and is there to be discarded.
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A man goes 9 km east, then 4 km north, then 5 km west and finally 4 km south. How far is he from his starting point ?
Answer: C
Correct answer: 4 km
Treat the two axes separately.
\[\text{East-west} = 9 - 5 = 4 \text{ km east}, \qquad \text{North-south} = 4 - 4 = 0\]
He ends 4 km due east of where he began.
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A dog runs 20 metre towards East and turns Right, runs 10 metre and turns to right, runs 9 metre and again turns to left, runs 5 metre and then turns to left, runs 12 metre and finally turns to left and runs 6 metre. Now which direction dog is facing ?
Answer: B
Correct answer: North
Starting eastward, the two right turns bring him first to south and then to west; the two left turns that follow bring him to south again and then to east - and the last left turn leaves him facing north.
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After walking 6 km, I turned to the right and then walked 2 km. After then I turned to the left and walked 10 km. In the end, I was moving towards the North. From which direction did I start my journey?
Answer: B
Correct answer: South
A right turn followed by a left turn leaves a walker facing the way he began, so his final direction is his first: north. Setting out northward means he started from the south.
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A person travels 6 km towards the north and then 8 km towards the east. What is the shortest distance from his starting point ?
Answer: D
Correct answer: 10 km
The two legs are at right angles, so the shortest distance is the hypotenuse.
\[d = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ km}\]
He has walked 14 km but ends only 10 km from the start.
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Amit started walking positioning his back towards the sun. After some time, he turned left, then turned right and towards the left again. In which direction is he going now?
Answer: A
Correct answer: North or South
With his back to the sun he is walking away from it, but we are not told whether it is morning or evening, so he may be heading west or east. A left turn, a right turn and a left turn amount to a quarter turn to the left, which brings him to face north or south according to which way he began.
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