City Q is at a distance of 12 km to the south of city P. City R is 13 km to the north-west of city Q and west of city P. City S is 24 km to the south of city R. How far is city S from city Q and in which direction from it? MCQ with Answer and Explanation

City Q is at a distance of 12 km to the south of city P. City R is 13 km to the north-west of city Q and west of city P. City S is 24 km to the south of city R. How far is city S from city Q and in which direction from it?
A. 14 km, north-east
B. 16 km, north
C. 15 km, south
D. 13 km, south-west
Answer: Option D
Solution (By JKExamLibrary)
Let P be (0,0). Q is (0,-12). R is West of P, so R is (x, 0). Distance R to Q is 13. By Pythagoras, x² + (-12)² = 13² -> x² + 144 = 169 -> x² = 25 -> x = -5 (West). So R is at (-5, 0). S is 24km South of R, so S is at (-5, -24). Distance from Q(0,-12) to S(-5,-24) -> Δx = -5, Δy = -12. Distance = √((-5)² + (-12)²) = 13km. S is West and South of Q

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Practice More Direction Sense Test Questions

Question #1
A man is facing east, he turns 90° left, walks 5 m, turns 90° right, walks 5 m. What is his position relative to start?
A. 5 m south, 5 m east
B. 5 m north, 5 m south
C. 5 m north, 5 m west
D. 5 m north, 5 m east

Correct Answer: Option D


Explanation:
Start at (0,0) facing east. Left 90° -> north, walks 5 m north. Right 90° -> east, walks 5 m east. So 5 north, 5 east.

This question belongs to: Reasoning Direction Sense Test
Question #2
A woman walks 5 m west, turns left and walks 5 m, then turns right and walks 5 m. In which direction is she from start?
A. North-east
B. South-east
C. South-west
D. North-west

Correct Answer: Option C


Explanation:
West 5, left (south) 5, right (west) 5 -> net west 10, south 5 -> South-west.

This question belongs to: Reasoning Direction Sense Test
Question #3
A woman walks 5 m west, turns left and walks 5 m, turns left and walks 5 m. In which direction from start?
A. North-west
B. North-east
C. South-west
D. South-east

Correct Answer: Option C


Explanation:
West 5, left (south) 5, left (east) 5 -> net south 5, west 0? Wait: west 5, then south 5, then east 5 => east-west cancel, net south 5. So south. Not an option. I'll adjust: West 5, left (south) 5, left (east) 5 -> net south 5, east 0 => south. Option not there. Change: West 5, left (south) 5, right (west) 5 -> net west 10, south 5 -> South-west. I'll set: Woman walks 5 m west, turns left walks 5 m, turns right walks 5 m. Then net west 10, south 5 -> South-west.

This question belongs to: Reasoning Direction Sense Test