From a point D Sarita Walked 50 metres to the North, then after turning to right walked 50 metres. She again turned right and walked another 70 metres and finally turned to right and walked 50 metres. In which direction and at what distance is she from the starting point D?
Correct Answer :
20 metres to the South
Solution :
The correct option is: 20 metres to the South.
Let us trace Sarita's movements step-by-step from the starting point D:
1. Initial position: Sarita starts at point D.
2. First movement: She walks 50 metres to the North. Let this new position be point A. Point A is 50 metres North of D.
3. Second movement: From A, she turns to her right (which is East) and walks 50 metres to reach point B. Point B is 50 metres East of A.
4. Third movement: From B, she turns right (which is South) and walks 70 metres to reach point C. Since she walks 70 metres South, she passes the latitude of D (which is 50 metres South of A/B) and goes an additional 20 metres South of D's latitude.
5. Fourth movement: From C, she turns right (which is West) and walks 50 metres to reach her final position, say point E.
Now, let us analyze the final position E relative to the starting point D:
- In the East-West direction: She walked 50 metres East (from A to B) and then 50 metres West (from C to E). Thus, she is back on the same North-South line as the starting point D.
- In the North-South direction: She walked 50 metres North (from D to A) and then 70 metres South (from B to C).
The net distance from the starting point D is:
Since the Southbound movement (70 metres) was greater than the Northbound movement (50 metres), her final position E is to the South of the starting point D.
Therefore, Sarita is 20 metres to the South from her starting point D.
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