📘 Quiz

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Question 1 / 20
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1
K is located 40 m South-West of L. If M is 40 m South-East of L, what is the direction of M from K?
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Solution: Step 1: Place L at the center of a compass or coordinate system for easy visualization. Step 2: K is 40 m South-West of L. This means K is located in the bottom-left quadrant relative to L. Step 3: M is 40 m South-East of L. This means M is located in the bottom-right quadrant relative to L. Step 4: Mentally or physically draw these points. L is the reference. K is down and left from L. M is down and right from L. Step 5: To determine the direction of M from K, imagine standing at K and looking towards M. Step 6: From K, you would need to move directly horizontally to the right to reach M, as both K and M are at the same 'South' level from L (implied by equal distance and South-West/South-East). Step 7: Therefore, M is in the East direction of K.
2
A person starts at point A, walks 12 meters north, then 10 meters east, followed by 12 meters south, and finally 5 meters east. What is the person's final position relative to the starting point?
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Solution: Step 1: Break down the movements: - 12 meters north - 10 meters east - 12 meters south - 5 meters east Step 2: Calculate net movement: - North-South movement: 12 meters north - 12 meters south = 0 meters - East movement: 10 meters + 5 meters = 15 meters east Step 3: Determine final position: The person ends up 15 meters east of the starting point. Step 4: Conclusion: The person is 15 meters towards the east from the starting point.
3
Person A is in the East of Person B and Person B is in the North of Person C. Person D is in the South of Person C. In which direction is Person A from Person D?
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Solution: Step 1: Understand the given directions. Step 2: Person A is east of Person B. Step 3: Person B is north of Person C. Step 4: Person D is south of Person C. Step 5: Visualize the positions: Person C is the reference point. Step 6: Person B is north, and Person D is south of Person C. Step 7: Person A, being east of Person B, will be northeast of Person C. Step 8: Comparing Person A and Person D's positions relative to Person C, Person A is southwest of Person D. Step 9: Hence, Person A is in the southwest direction of Person D.
4
Hemant, departing from his house in the east, arrived at a crossing on his way to the university. At this crossing, the road on his left leads to a theatre, and the road directly ahead leads to a hospital. In which direction is the university located?
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Solution: Step 1: Hemant starts from his house in the east and arrives at a crossing. This means he approached the crossing from the East, or if he is at the crossing, his house is to the East relative to the crossing. Thus, he would be facing West if his house is behind him. Step 2: If Hemant is facing West at the crossing: * The road to his left would be pointing South (West -> Left is South). * The road straight ahead would be pointing West. Step 3: The problem states that the road to his left (South) leads to a theatre, and the road straight ahead (West) leads to a hospital. Step 4: The only remaining main direction is to his right, which would be North (West -> Right is North). Step 5: Therefore, the university is in the North direction.
5
Village Q is located North of village P. Village R is situated East of village Q. Village S is positioned to the left of village P. In what direction is village S with respect to village R?
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Solution: Step 1: Let's set village P as the origin (0,0). Step 2: 'Village Q is to the North of P.' So, Q is at (0, y_Q) where y_Q > 0. For simplicity, let Q = (0,1). Step 3: 'Village R is in the East of Q.' So, R is at (x_R, 1) where x_R > 0. For simplicity, let R = (1,1). Step 4: 'Village S is to the left of P.' In geographical context, 'left of' typically means West of. So, S is at (x_S, 0) where x_S < 0. For simplicity, let S = (-1,0). Step 5: Now, we need to find the direction of S (-1,0) with respect to R (1,1). Step 6: To go from R (1,1) to S (-1,0): * The x-coordinate changes from 1 to -1 (decrease), indicating Westward movement. * The y-coordinate changes from 1 to 0 (decrease), indicating Southward movement. Step 7: Therefore, village S is in the South-West direction with respect to village R.
6
One morning, Sujata began walking towards the Sun. After walking a certain distance, she turned right, then turned right again, and after covering more distance, she turned right a third time. In what direction is she currently facing?
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Solution: Step 1: Determine Sujata's initial direction. One morning, the sun rises in the East. So, Sujata started walking towards the East. Step 2: Initial direction: East. Step 3: First turn: She turned right from East. Turning right from East means she is now facing South. Step 4: Second turn: She turned right again from South. Turning right from South means she is now facing West. Step 5: Third turn: She turned right a third time from West. Turning right from West means she is now facing North. Step 6: Therefore, Sujata is finally facing North.
7
An individual, X, began walking directly South. After covering 5 meters, X turned left and proceeded for 3 meters. Following this, X turned right and walked an additional 5 meters. In which direction is X currently facing?
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Solution: Step 1: X starts by walking towards the South. The current facing direction is South. Step 2: After walking 5m, X turns to the left. When facing South, a left turn leads to facing East. Step 3: X walks 3m while facing East. The current facing direction is East. Step 4: X then turns to the right. When facing East, a right turn leads to facing South. Step 5: X walks 5m while facing South. Step 6: Therefore, X is currently facing South.
8
One evening, before sunset, Rekha and Hema were conversing face to face. If Hema's shadow appeared exactly to Hema's right, what direction was Rekha facing?
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Solution: Step 1: Determine the sun's position and the general direction of shadows in the evening. In the evening, the sun sets in the West. Step 2: Consequently, any shadow will fall towards the East. Step 3: The problem states that Hema's shadow was exactly to Hema's right. Step 4: This implies that Hema's right side is pointing towards the East. Step 5: If a person's right side is East, that person must be facing North. So, Hema is facing North. Step 6: Rekha and Hema are talking to each other face to face. If Hema is facing North, then Rekha, who is facing Hema, must be facing the opposite direction. Step 7: Therefore, Rekha was facing South.
9
After traversing 6 km, I turned right and then walked 2 km. Subsequently, I turned left and walked 10 km. If, at the journey's end, I was moving North, what was my initial starting direction?
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Solution: Step 1: Let's analyze the sequence of movements in reverse, knowing the final facing direction. Step 2: In the end, I was moving towards the North. Step 3: Before moving North, I turned to the left. To face North after turning left, I must have been facing East prior to that turn. Step 4: Before facing East, I turned to the right. To face East after turning right, I must have been facing North prior to that turn. Step 5: This 'North' was the direction I was facing after completing the initial 6 km walk. Thus, the direction in which I started my journey and walked the first 6 km was North. Step 6: Based on standard directional logic, if the final direction is North, and the net effect of a Right turn followed by a Left turn is no change in orientation, then the initial direction must also be North. Note: The provided correct answer is 'South'. However, based on the logical derivation of the problem statement, the starting direction would be North. If the correct answer is indeed 'South', there might be an alternative interpretation of the turns or a specific context not provided in the problem statement that leads to this conclusion. For this solution, we adhere to the standard logical interpretation.
10
Shyam begins walking 5 km East, then turns left and walks 6 km. He turns right again and walks 9 km. Finally, he turns right once more and walks 6 km. What is Shyam's current straight-line distance from his starting point?
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Solution: Step 1: Assume Shyam's starting point is the origin (0,0). Step 2: Walks 5 km East: Position (5,0). Facing East. Step 3: Turns left (North) and walks 6 km: Position (5,6). Facing North. Step 4: Turns right (East) and walks 9 km: Position (5+9, 6) = (14,6). Facing East. Step 5: Turns right (South) and walks 6 km: Position (14, 6-6) = (14,0). Facing South. Step 6: Shyam's final position is (14,0). His starting point is (0,0). Step 7: The distance from the starting point is the straight-line distance between (14,0) and (0,0). Step 8: Distance = sqrt((14-0)^2 + (0-0)^2) = sqrt(14^2) = 14 km.
11
One morning after sunrise, Suresh was standing facing a pole. The pole's shadow fell precisely to Suresh's right. In which direction was Suresh facing?
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Solution: Step 1: In the morning, after sunrise, the sun is positioned in the East. Step 2: Consequently, any shadow cast during this time will fall towards the West. Step 3: The problem states that the shadow of the pole fell exactly to Suresh's right. Step 4: This implies that Suresh's right hand is pointing towards the West, which is the direction where the shadow is. Step 5: If a person's right hand is pointing West, then that person must be facing South (because if you face South, your right is West). Step 6: Therefore, Suresh was facing South.
12
One morning, Udai and Vishal conversed while facing each other at an intersection. If Vishal's shadow fell precisely to Udai's left, what direction was Udai facing?
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Solution: Step 1: Understand the position of the sun in the morning. In the morning, the sun rises in the East. Step 2: Therefore, any shadow will fall towards the West. Step 3: The problem states Vishal's shadow was exactly to the left of Udai. Step 4: This implies that Udai's left side is in the West direction. Step 5: If Udai's left is West, then Udai must be facing North. Step 6: Verify the scenario: If Udai faces North, his left is West, and his right is East. If Vishal is facing Udai, Vishal must be facing South. Vishal's shadow falls to the West. For Udai (facing North), West is indeed to his left. This confirms the condition. Step 7: Udai was facing North.
13
Rohit walked 25 m South. He then turned left and walked 20 m. Next, he turned left again and walked 25 m. Finally, he turned right and walked 15 m. What is Rohit's distance and direction from his starting point?
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Solution: Step 1: Assume Rohit's starting point is the origin (0,0). Step 2: Walks 25 m South: Position (0, -25). Facing South. Step 3: Turns left (East) and walks 20 m: Position (20, -25). Facing East. Step 4: Turns left (North) and walks 25 m: Position (20, -25 + 25) = (20, 0). Facing North. Step 5: Turns right (East) and walks 15 m: Position (20 + 15, 0) = (35, 0). Facing East. Step 6: Rohit's final position is (35,0). His starting point is (0,0). Step 7: The distance from the starting point is the magnitude of the final position's coordinates, which is 35 m. Step 8: The direction from the starting point is determined by the coordinates (35,0), which is purely along the positive X-axis. Step 9: Therefore, Rohit is 35 m East from his starting point.
14
A person starts from their house, walks 10 km south, then 5 km west, takes a left turn, and walks 7 km to reach school. In which direction is the house from the school?
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Solution: Step 1: The person starts at their house. Step 2: They walk 10 km south. Step 3: Then, they walk 5 km west. Step 4: After that, they walk 7 km south. Step 5: To find the direction from the school to the house, reverse the steps. Step 6: First, go 7 km north. Step 7: Then, go 5 km east. Step 8: Finally, go 10 km north. Step 9: This results in being 5 km east and 17 km north of the starting point. Step 10: Therefore, the house is North-East of the school.
15
If South is related to North-West, then West is related to which direction, following the same rotational principle?
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Solution: Step 1: Determine the rotational relationship from 'South' to 'North-West'. Assume standard compass degrees: North=0°, East=90°, South=180°, West=270°, North-West=315°. To go from South (180°) to North-West (315°) clockwise, the rotation is 315° - 180° = 135°. Step 2: Apply the same 135° clockwise rotation to 'West'. West is 270°. Rotating 135° clockwise: 270° + 135° = 405°. Step 3: Since a full circle is 360°, subtract 360° from 405°: 405° - 360° = 45°. Step 4: The direction corresponding to 45° is 'North-East'.
16
Y is situated East of X, and X is North of Z. If P is South of Z, what is the direction of P relative to Y?
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Solution: Step 1: Visualize the positions relative to each other. Step 2: 'X is in the North of Z': Imagine Z at the bottom, and X directly above it. Step 3: 'Y is in the East of X': Imagine Y to the right of X. So, from a top-down view, you have Z, then X directly above Z, and Y to the right of X. Step 4: 'P is in the South of Z': Imagine P directly below Z. Step 5: Now, determine the direction of P from Y. From Y, you would need to move left (West) and then down (South) to reach P. Step 6: Therefore, P is in the South-West direction of Y.
17
Sundar runs 20 m East, then turns right and runs 10 m. He then turns right again and runs 9 m. After another right turn, he runs 5 m. Subsequently, he turns left and runs 12 m, and finally, he turns right and runs 6 m. In which direction is Sundar currently facing?
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Solution: Step 1: Sundar starts by running towards East. Current facing direction: East. Step 2: Turns right. When facing East, a right turn means facing South. Current facing direction: South. Step 3: Turns right again. When facing South, a right turn means facing West. Current facing direction: West. Step 4: Turns right again. When facing West, a right turn means facing North. Current facing direction: North. Step 5: Turns left. When facing North, a left turn means facing West. Current facing direction: West. Step 6: Turns right. When facing West, a right turn means facing North. Current facing direction: North. Step 7: Therefore, Sundar is finally facing North.
18
Given the following directional codes: 'A x B' means A is South of B; 'A + B' means A is North of B; 'A % B' means A is East of B; 'A - B' means A is West of B. In the expression P % Q + R - S, what is the direction of S with respect to Q?
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Solution: Step 1: Decode each part of the expression P % Q + R - S. * P % Q: P is to the East of Q. (This means Q is to the West of P) * Q + R: Q is to the North of R. (This means R is to the South of Q) * R - S: R is to the West of S. (This means S is to the East of R) Step 2: Create a mental or physical map based on these relationships. * From 'Q + R', R is South of Q. * From 'P % Q', P is East of Q. * From 'R - S', S is East of R. Step 3: Combine these relationships to determine the position of S relative to Q. * Place Q. R is directly South of Q. * S is East of R. So, from R, go East to reach S. * Therefore, from Q, you first go South to R, and then East to S. Step 4: This combined movement means S is in the South-East direction with respect to Q.
19
Amit started walking with his back facing the sun. After some time, he turned left, then turned right, and then turned left again. In which direction is Amit currently walking?
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Solution: Step 1: Analyze the initial condition 'positioning his back towards the sun'. * If it is morning (sun in the East), facing with back to the sun means Amit is facing West. * If it is evening (sun in the West), facing with back to the sun means Amit is facing East. Step 2: Analyze the sequence of turns: 'turned left, then turned right, and towards the left again'. * A left turn (L) followed by a right turn (R) cancels out (L + R = no net change in orientation). * So, the sequence 'L, then R, then L' is equivalent to a single Left turn from the initial facing direction. Step 3: Apply the net turn to both possible initial directions. * Case 1: If Amit started facing West (morning scenario), after a single Left turn, he would be facing South (West -> Left is South). * Case 2: If Amit started facing East (evening scenario), after a single Left turn, he would be facing North (East -> Left is North). Step 4: Since the time of day (morning or evening) is not specified, there are two possible final directions. Step 5: Therefore, Amit is now going either North or South.
20
Four friends, A, B, C, and D, reside in the same area. B's house is situated to the East of A's house, but also to the North of C's house. C's house is located to the West of D's house. In which direction is D's house from A's house?
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Solution: Step 1: Let's set A's house as the reference point, (0,0). Step 2: 'B is in the East of A's house.' This means B is to the right of A. Let A = (0,0) and B = (x,0) where x > 0. For simplicity, let B = (1,0). Step 3: 'B is in the North of C's house.' This means C is to the South of B. If B = (1,0), then C = (1,y) where y < 0. For simplicity, let C = (1,-1). Step 4: 'C is in the West of D's house.' This means D is to the East of C. If C = (1,-1), then D = (z,-1) where z > 1. For simplicity, let D = (2,-1). Step 5: Now, compare D's position (2,-1) with A's position (0,0). Step 6: The positive x-coordinate (2) indicates East, and the negative y-coordinate (-1) indicates South. Step 7: Therefore, D's house is in the South-East direction of A's house.
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