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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A man walks 5 km toward south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place?
Answer: D
Correct answer: South-West
He goes 5 km south, turns right to face west and goes 3 km, then turns left to face south again and goes 5 km. Altogether he is 10 km south and 3 km west of where he began - that is, to the south-west.
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A is to the north of B, and C is to the east of B. In which direction is C from A ?
Answer: A
Correct answer: South-East
Place B at the origin, so A lies directly above it and C directly to its right. Seen from A, the point C is both to the right and lower down.
That combination of east and south gives the south-east direction.
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Some boys are sitting in three rows all facing North such that A is in the middle row. P is just to the right of A but in the same row. Q is just behind of P while R is in the North of A. In which direction of R is Q?
Answer: D
Correct answer: South-East
All three rows face north, so a person’s right hand points east. P is therefore east of A, and Q, being just behind P, is south of P. R stands north of A. Q is thus both east of and south of R - that is, to R’s south-east.
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Umesh directly went from P, to Q which is 9 feet distant. Then he turns to the right and walked 4 feet. After this he turned to the right and walked a distance which is equal from P to Q. Finally he turned to the right and walked 3 feet. How far is he now from P?
Answer: C
Correct answer: 1 feet
P to Q is 9 feet; he then goes 4 feet at right angles, 9 feet back the way he came, and finally turns right for the last leg. The two 9-foot legs cancel, so what remains is the difference between the 4-foot leg and the last one - 1 foot.
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One morning after sunrise, Suresh was standing facing a pole. The shadow of the pole fell exactly to his right. To which direction was he facing?
Answer: C
Correct answer: South
After sunrise the sun is in the east, so every shadow points west. The pole’s shadow fell to Suresh’s right, so west was on his right hand - which puts him facing south.
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'P' walked 1 km towards south direction and turned 90ºACW and walked 2 km. Then he turned his left and walked 1 km and then he turned his right and walked 2 km. After that he turned 90º ACW and walked 3 km. How far is he from the starting point ?
Answer: A
Correct answer: 5 km
Anticlockwise from south is east, not west - that is the step this item turns on. From the origin: 1 km south gives \( (0,-1) \); turning 90 degrees anticlockwise to face east, 2 km gives \( (2,-1) \); a left turn faces north, so 1 km gives \( (2,0) \); a right turn faces east, so 2 km gives \( (4,0) \); and a final anticlockwise turn faces north, so 3 km gives \( (4,3) \). The distance is \[ \sqrt{4^2+3^2} = 5\ \mathrm{km}. \]
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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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