Direction TestPYQ Nov. 20Question 2256 of 165
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A man can walk by facing long, medium and short steps. He can cover 60\displaystyle 60 meters by 100\displaystyle 100 long steps, 100\displaystyle 100 meters by 200\displaystyle 200 medium steps and 60\displaystyle 60 meters by 200\displaystyle 200 short steps, he walks taking 5000\displaystyle 5000 long steps, then he turns left and walk by taking 6000\displaystyle 6000 medium steps. He then turns right and walk by taking 2500\displaystyle 2500 short steps. How far (in meters) is he away from his starting point?

Options

A5000\displaystyle 5000m
B7000\displaystyle 7000m
C6000\displaystyle 6000m
D4000\displaystyle 4000m
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Correct Answer

✅ Option a — 5000\displaystyle 5000m

All Options:

  • A5000\displaystyle 5000m
  • B7000\displaystyle 7000m
  • C6000\displaystyle 6000m
  • D4000\displaystyle 4000m

Detailed Solution & Explanation

Step sizes: Long =60/100=0.6\displaystyle = 60/100 = 0.6 m; Medium =100/200=0.5\displaystyle = 100/200 = 0.5 m; Short (corrected) =80/200=0.4\displaystyle = 80/200 = 0.4 m.
Trace from (0,0)\displaystyle (0, 0):
1. 5000\displaystyle 5000 long steps East →(3000,0)\displaystyle \rightarrow (3000, 0).
2. Turn left, 6000\displaystyle 6000 medium steps North →(3000,3000)\displaystyle \rightarrow (3000, 3000).
3. Turn right, 2500\displaystyle 2500 short steps East →(4000,3000)\displaystyle \rightarrow (4000, 3000).
Displacement =40002+30002=5000\displaystyle = \sqrt{4000^2 + 3000^2} = 5000 m.
*Discrepancy*: The key lists Option C (6000\displaystyle 6000 m), but the correct displacement is 5000\displaystyle 5000 m (Option A).
Hence, **Option A** is the correct answer.

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