Gita starts from point A and walks 1000 m east. She then walks 800 m north, followed by 640 m west and 512 m south, reaching point B. After this, she continues moving in the same cyclic order: east,…
Question and options
Gita starts from point A and walks 1000 m east. She then walks 800 m north, followed by 640 m west and 512 m south, reaching point B. After this, she continues moving in the same cyclic order: east, north, west, south, with each successive movement 20% shorter than the previous one. After infinitely many such moves, approximately how far in meters will Gita be from her starting point A?
- 711
- 800
- 765
- 781
Answer and explanation
Correct answer: D - 781
Moves form a GP with ratio 0.8 rotating by 90 deg. Net east = 1000(1 - 0.64 + 0.64^2 - ...) = 1000/1.64 = 609.8; net north = 800/1.64 = 487.8. Distance = sqrt(609.8^2 + 487.8^2) = 1000/sqrt(1.64) = approx 781 m.
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