One morning after sunrise Nivedita and Niharika were talking to each other face to face at Dalphin crossing. If Niharika's shadow was exactly to the right of Nivedita, Which direction Niharika was facing?
Answer: A
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In the morning sun rises in the East. Hence then any shadow falls in the West. Since Nikharia's shadow was exactly to the right of Nivedita. Hence Nikharia is facing towards North.
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A man walks 2 km towards North. Then he turns to East and walks 10 km. After this he turns to North and walks 3 km. Again he turns towards East and walks 2 km. How far is he from the starting point?
Answer: B
Correct answer: 13 km
The northward legs come to \( 2 + 3 = 5 \) km and the eastward to \( 10 + 2 = 12 \) km. By Pythagoras the distance is \[ \sqrt{5^2 + 12^2} = \sqrt{169} = \mathbf{13}\text{ km} \]
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Starting from the point X, Jayant walked 15 m towards west. He turned left and walked 20 m. He then turned left and walked 15 m. After this he turned to his right and walked 12 m. How far and in which directions is now Jayant from X?
Answer: A
Correct answer: 32 m, South
Adding the legs: west 15, then south 20, then east 15, then south 12. The east and west cancel, leaving \( 20 + 12 = 32 \) metres. So Jayant is 32 m south of X.
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Y is in the East of X which is in the North of Z. If P is in the South of Z, then in which direction of Y, is P?
Answer: D
Correct answer: None of these
Put X at the origin. Y lies east of X, Z lies south of X, and P lies south of Z - so P is directly south of X and Y is to its east. P therefore lies to the south-west of Y, which is not among the choices offered.
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Ravi started walking from his house east direction on Bus stop which is 3km.away. Then he set off in the bus straight towards his right to the school 4 km away. what is the crow flight distance from his house to the school?
Answer: B
Correct answer: 5 km
The two legs are at right angles - east 3 km, then a right turn onto south for 4 km - so the straight-line distance is the hypotenuse: \[ \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\ \mathrm{km}. \] The 7 km offered is the distance actually travelled along the roads, which is what the phrase “as the crow flies” exists to exclude.
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A man walks 5 km toward south and then turns to the right. After walking 3 km he turns to the left and walks 4 km. And then he goes back 10 km straight. Now in which direction is he from the starting place ?
Answer: B
Correct answer: North-West
Track the turns one at a time. He starts south for 5 km, turns right to face west and covers 3 km, turns left to face south again for 4 km, and then goes back - reversing his heading to north - for 10 km. Southward he has gone \( 5+4=9 \) km and northward 10 km, so he ends 1 km north of his start and 3 km west of it. That puts him north-west of the starting place.
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One morning sujata started to walk towards the Sun. After covering some distance she turned to right then again to the right and after covering some distance she again turns to the right. Now in which direction is she facing?
Answer: A
Correct answer: North
Walking towards the morning sun means walking east. Turning right takes her south, right again west, and right a third time north.
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A man facing north turns 90 degrees clockwise, then turns 180 degrees, and then turns 90 degrees anticlockwise. Which direction is he facing now ?
Answer: A
Correct answer: South
Take the turns in order: north turned 90 degrees clockwise gives east; east turned 180 degrees gives west; west turned 90 degrees anticlockwise gives south.
So he ends up facing south, exactly opposite to his original direction.
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I travel 20 miles towards north and then travel 25 miles eastward. I then travel 40 miles rightwards, then travel 30 miles towards right and then travel 12 miles to the left and finally 20 miles northwards. How far am I approximately from my original starting point and in what direction ?
Answer: B
Correct answer: 13 miles towards south-west
Take the start as the origin with east and north positive. North 20 gives \( (0,20) \); east 25 gives \( (25,20) \); facing east, a right turn faces south, so 40 gives \( (25,-20) \); another right turn faces west, so 30 gives \( (-5,-20) \); facing west, a left turn faces south, so 12 gives \( (-5,-32) \); and 20 north gives \( (-5,-12) \). The distance is \[ \sqrt{5^2+12^2} = \sqrt{169} = 13\ \mathrm{miles}, \] and being west and south of the origin, the direction is south-west.
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Village Q is to the North of the village P. The village R is in the East of Village Q. The village S is to the left of the village P. In which direction is the village S with respect to village R?
Answer: B
Correct answer: South-West
Take P at the origin. Q lies north of P and R east of Q, so R is to the north-east. S lies to P’s left, that is west of P. S is therefore both west of and south of R - to R’s south-west.
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