Question 34

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?

Name: 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?
Uploaded: 2026-05-21T10:45:16.759706+05:30
Duration: 10 min 59 s
Description: 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?

Solution

The walk pattern is an infinite spiral: leg $$n$$ has length $$1000 \cdot 0.8^{n-1}$$, directions cycle E, N, W, S.

Net East: $$\dfrac{1000 - 640}{1 - 0.8^4} = \dfrac{360}{0.5904} \approx 609.76$$.

Net North: $$\dfrac{800 - 512}{1 - 0.8^4} = \dfrac{288}{0.5904} \approx 487.81$$.

Distance $$AB = \sqrt{609.76^2 + 487.81^2} \approx \sqrt{609766} \approx \mathbf{781}$$.

Get AI Help

Video Solution

Create a FREE account and get:

Download Maths Shortcuts PDF
Get 300+ previous papers with solutions PDF
500+ Online Tests for Free

Solution

Get AI Help

Video Solution

Over 8000+ registered students have benefitted from Cracku's IPMAT & IIMB UG coursesIPMAT Course

Download resources