This is a question on direction sense. Let's break down Sunita's journey step-by-step to determine her final distance from her starting point.
- Step 1: 6 km Northeast: Draw a starting point. From this point, draw a line at a 45-degree angle (northeast) and mark 6 km along it.
- Step 2: 9 km West: From the end of the first line, draw a line to the west (left) and mark 9 km.
- Step 3: 6 km Southwest: From the end of the second line, draw a line at a 45-degree angle (southwest) and mark 6 km.
- Step 4: 3 km East: From the end of the third line, draw a line to the east (right) and mark 3 km.
Now, observe the final position. Notice that the west-east movements cancel each other out to some degree. The net westward movement is 9km - 3km = 6km. The northeast movement forms a right-angled triangle with the base (west). To find the total distance, consider the displacement in the north-south direction and the displacement in the east-west direction. The net northward displacement would be approximately \(6 \cos(45^\circ)\) which is approximately 4.24 km. The net westward displacement is 6km.
We can think of this as a right-angled triangle with one side being approximately 4.24 km (North) and another side being 6 km (West). Using the Pythagorean theorem (a² + b² = c²), we can find the distance from the starting point:
Distance² = 4.24² + 6²
Distance² ≈ 17.98 + 36 = 53.98
Distance ≈ √53.98 ≈ 7.35 km
However, let's simplify the problem. If we consider the components of each movement:
- Northeast 6km: approximately 4.24 km North and 4.24 km East
- West 9km: 9km West
- Southwest 6km: approximately 4.24 km South and 4.24 km West
- East 3km: 3 km East
Adding up the East-West components: 4.24 - 9 - 4.24 + 3 = -6km (6km West)
Adding up the North-South components: 4.24 - 4.24 = 0km
Therefore, she is approximately 6 km away from her initial position.
Why other options are incorrect:
- 3 km: This significantly underestimates the distance traveled.
- 9 km: This is closer, but doesn't account for the net effect of all movements.
- 12 km: This overestimates the distance travelled.
Therefore, the closest answer is 6 km.
Similar Questions
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All fruits are wines.
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Important Questions from Conventional Syllogism
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I. Some blue are red.
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II. No red is green.
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Statement 1 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
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Conclusion III : All cars are buses.
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Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
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