Reasoning Ability — MCQ Practice Questions & Answers

Question 1

Rahul starts from point A and walks 10 km towards the North. He then turns right and walks 15 km. After this, he turns left and walks 8 km. Finally, he turns right and walks 12 km to reach point B. What is his net displacement from point A in terms of direction?

Accepted Answer

Correct answer: A. 27 km towards North-East — Step 1: Establish Coordinate System and Track North-South Movement Let point A be at origin (0, 0). North is positive y-direction, East is positive x-direction. Starting position: (0, 0) - Walks 10 km North: position becomes (0, 10) - Turns right (now facing East) and walks 15 km: position becomes (15, 10) - Turns left (now facing North) and walks 8 km: position becomes (15, 18) - Turns right (now facing East) and walks 12 km: position becomes (27, 18) 	ext{Final position B} = (27, 18) Step 2: Calculate Net Displacement The net displacement is the straight-line distance from point A to point B using the Pythagorean theorem. 	ext{Displacement} = \sqrt{(27-0)^2 + (18-0)^2} = \sqrt{27^2 + 18^2} = \sqrt{729 + 324} = \sqrt{1053} = \sqrt{729 + 324} = \sqrt{1053} \approx 32.45 	ext{ km} Step 3: Determine Direction of Displacement Find the angle from North towards East using trigonometry. 	an(	heta) = \frac{	ext{East component}}{	ext{North component}} = \frac{27}{18} = \frac{3}{2} = 1.5 	heta = \arctan(1.5) \approx 56.3° This means the di

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B. 25 km towards East-North-East

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C. 23 km towards North-East

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D. 20 km towards East

Question 2

A person is standing at the origin of a coordinate system. He walks 5 km South, then 12 km West, then 9 km North, and finally 7 km East. At which direction is he now with respect to his starting point?

Accepted Answer

Correct answer: A. South-West — Step 1: Track the North-South displacement Starting at origin (0, 0), walking 5 km South gives position (0, -5), then 9 km North gives displacement of -5 + 9 = 4 km North. 	ext{Net North-South} = -5 + 9 = 4 	ext{ km North} Step 2: Track the East-West displacement Walking 12 km West gives position (-12, 4), then 7 km East gives displacement of -12 + 7 = -5 km (or 5 km West). 	ext{Net East-West} = -12 + 7 = -5 	ext{ km (5 km West)} Step 3: Determine final position and direction The final position is 5 km West and 4 km North of the starting point. Since the person is West and North of the origin, the direction is North-West. 	ext{Final position} = (-5, 4) 	ext{ km} **The person is now in the North-West direction with respect to the starting point, not South-West as given in option A. However, if the answer key states South-West, there may be an error in either the problem statement or the provided answer.**

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B. North-West

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C. South-East

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D. North-East

Question 3

Priya faces North. She turns 90° clockwise, then 45° counter-clockwise, then 135° clockwise. Finally, she turns 90° counter-clockwise. Which direction is she facing now?

Accepted Answer

Correct answer: C. South — Step 1: Initial Position and First Turn Priya starts facing North. She turns 90° clockwise. 	ext{North} + 90° 	ext{ clockwise} = 	ext{East} Step 2: Second and Third Turns Combined From East, she turns 45° counter-clockwise, then 135° clockwise. 45° 	ext{ counter-clockwise} - 135° 	ext{ clockwise} = -90° 	ext{ (net clockwise)} 	ext{East} + 90° 	ext{ clockwise} = 	ext{South} Step 3: Final Turn From South, she turns 90° counter-clockwise. 	ext{South} + 90° 	ext{ counter-clockwise} = 	ext{East} **Priya is now facing East, not South. However, if we verify the total rotation: North → 90° CW → 45° CCW → 135° CW → 90° CCW gives a net rotation of 90° clockwise from North, which is East.** Note: The given answer of South appears to be incorrect based on the step-by-step calculation. The correct answer should be East.

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A. North-West

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B. East

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D. South-West

Question 4

In a city grid, Apartment A is 4 km directly East of Apartment B. Apartment C is 3 km directly North of Apartment B. Apartment D is 2 km directly West of Apartment C. From Apartment D, if you travel in a straight line to Apartment A, what is the total distance covered and the general direc

Accepted Answer

Correct answer: C. √29 km in East-South-East direction — Step 1: Establish Coordinate System Let Apartment B be at the origin (0, 0). Apartment A is 4 km East, so A is at (4, 0). Apartment C is 3 km North of B, so C is at (0, 3). Apartment D is 2 km West of C, so D is at (-2, 3). 	ext{Coordinates: } B(0,0), A(4,0), C(0,3), D(-2,3) Step 2: Calculate Distance from D to A Using the distance formula between points D(-2, 3) and A(4, 0): d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d = \sqrt{(4 - (-2))^2 + (0 - 3)^2} = \sqrt{(6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45} \sqrt{45} = \sqrt{9 	imes 5} = 3\sqrt{5} \approx 6.71 	ext{ km} Step 3: Determine Direction from D to A The displacement vector from D to A is (6, -3), meaning 6 km East and 3 km South. The angle from East toward South is calculated as: 	an(	heta) = \frac{3}{6} = \frac{1}{2} 	heta \approx 26.57° 	ext{ South of East, which is East-South-East direction} **The

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A. 5 km in South-East direction

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B. √37 km in South-East direction

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D. 6 km in South-East direction

Question 5

A ship starts from port X and sails 60 km towards North-East (exactly 45° from North). It then turns and sails 80 km towards South-East (exactly 45° from South). How far is the ship from port X?

Accepted Answer

Correct answer: D. 20√13 km — Step 1: Establish coordinate system and resolve first displacement Set port X at origin with North as positive y-axis and East as positive x-axis. The ship sails 60 km at 45° from North towards North-East. x_1 = 60 \sin(45°) = 60 	imes \frac{1}{\sqrt{2}} = \frac{60}{\sqrt{2}} = 30\sqrt{2} 	ext{ km} y_1 = 60 \cos(45°) = 60 	imes \frac{1}{\sqrt{2}} = \frac{60}{\sqrt{2}} = 30\sqrt{2} 	ext{ km} Step 2: Resolve second displacement from new position The ship then sails 80 km at 45° from South towards South-East. This means 45° East of South direction, or equivalently, the angle is -45° from East (or 315° from North). x_2 = 80 \sin(45°) = 80 	imes \frac{1}{\sqrt{2}} = \frac{80}{\sqrt{2}} = 40\sqrt{2} 	ext{ km} y_2 = -80 \cos(45°) = -80 	imes \frac{1}{\sqrt{2}} = \frac{-80}{\sqrt{2}} = -40\sqrt{2} 	ext{ km} Step 3: Calculate total displacement and distance from port X Total displacement components from port X: x_{total} = x_1 + x_2 = 30\sqrt{2} + 40

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A. 100 km

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B. 140 km

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C. 70 km

Question 6

Amit starts walking from point A towards North. After walking 10 km, he turns right and walks 5 km. Then he turns left and walks 8 km. Finally, he turns right and walks 3 km to reach point B. In which direction is point B with respect to point A?

Accepted Answer

Correct answer: A. North-East — Tracking Amit's movements: Starting North, he goes 10 km North; turns right (East) and walks 5 km; turns left (North) and walks 8 km; turns right (East) and walks 3 km. His net displacement is 8 km North and 8 km East (5+3), placing point B in the North-East direction from point A.

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B. East

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C. South-East

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D. North-West

Question 7

Three friends P, Q, and R are standing in a line. Q is to the West of P. R is to the South of Q. If R walks 10 meters North and then 5 meters East, he will be at the same position as Q. How far is P from R in the North-South direction?

Accepted Answer

Correct answer: B. 10 meters — Since R reaches Q's position by walking 10 meters North and 5 meters East, this means R was initially 10 meters South of Q and 5 meters West of Q. Given Q is West of P and they're in a line, P is East of Q. Therefore, P is 10 meters North of R in the North-South direction.

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A. 5 meters

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C. 15 meters

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D. Cannot be determined

Question 8

A person standing at origin moves 4 units North, then 3 units West, then 5 units South, then 2 units East, and finally 1 unit North. After these movements, if he turns 45 degrees clockwise from his current facing direction (which is North), which direction will he face?

Accepted Answer

Correct answer: A. North-East — The person's final position relative to origin is: North (4-5+1=0), West (3-2=1). His current facing direction remains North. Turning 45 degrees clockwise from North results in facing North-East direction.

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B. South-East

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C. North-West

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D. South-West

Reasoning Ability - MCQ Practice Questions