Village P is 20 km west of village Q, and village R is 15 km north of Q. What is the shortest distance between P and R ?
Answer: C
Correct answer: 25 km
P and R lie at the ends of two perpendicular arms meeting at Q, so the direct distance is the hypotenuse.
\[d = \sqrt{20^2 + 15^2} = \sqrt{400 + 225} = \sqrt{625} = 25 \text{ km}\]
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A person walks 5 km towards the south, turns left and walks 3 km, then turns left again and walks 5 km. How far is he from his starting point ?
Answer: B
Correct answer: 3 km
Facing south, a left turn points him east; after 3 km east, another left turn points him north. The 5 km south and 5 km north cancel, leaving 3 km east.
\[\text{Distance from start} = 3 \text{ km}\]
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P started from his house towards west. After walking a distance of 25 m. He turned to the right and walked 10 m. He then again turned to the right and walked 15 m. After this he is to turn right at 135o and to cover 30 m. In which direction should he go?
Answer: C
Correct answer: South-West
He walks west, turns right to face north, then right again to face east. Turning right through 135° from east swings him past south to the south-west, which is the direction of his last leg.
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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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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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Ravi walks 12 m towards the west, turns right and walks 5 m, then turns right again and walks 12 m. How far and in which direction is he from his starting point ?
Answer: B
Correct answer: 5 m north
From west, a right turn faces him north; after 5 m, another right turn faces him east. The 12 m west and 12 m east cancel.
\[\text{Net displacement} = 5 \text{ m towards the north}\]
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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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At sunrise, a man is walking and finds his shadow falling exactly to his right. Which direction is he facing ?
Answer: B
Correct answer: South
The sun rises in the east, so shadows at sunrise point towards the west. If west lies to his right, then he must be facing south, since a person facing south has west on the right hand.
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Ravi wants to go to the university. He starts from his home which is in the East and comes to a crossing. The road to the left ends in a theatre, straight ahead is the hospital. In Which direction is the University?
Answer: A
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Starting from his house in the East, Ravi moves westwards. Then, the theatre, which is to the left, will be in the south. The Hospital, which is straight ahead, will be to the West. So, the University will be to the North.
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A horse is facing north. It turns 90 degrees in the clockwise direction, then 180 degrees in the anti-clockwise and then another 90 degrees in the same direction. Which direction is the horse facing now?
Answer: B
Starting from the initial point facing north, the horse turns 90 degrees clockwise, which means it turns towards East. Similarly, the other directions can be considered and written as : EWS Thus, the direction it is facing now is South.
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