Kabita walks from her office 2 km to the east, then 8 km towards her right, then 2 km towards the east and then 4 km Kabita walks from her office 2 km to the east, then 8 km towards her right, then 2 km towards the east and then 4 km towards the south. Finally she turns left and walks 1 km to reach her apartment. The shortest aerial distance between Kabita’s office and her apartment is

Question:

Kabita walks from her office 2 km to the east, then 8 km towards her right, then 2 km towards the east and then 4 km towards the south. Finally she turns left and walks 1 km to reach her apartment. The shortest aerial distance between Kabita’s office and her apartment is: 

    (A) 25 km 

    (B) 13 km 

    (C) 12 km 

    (D) 17 km


Solution:



  1. Given,

    • Kabita walks 2 km east.
    • Then, she turns right (south) and walks 8 km.
    • Next, she walks 2 km east again.
    • Then, she turns south and walks 4 km.
    • Finally, she turns left (east) and walks 1 km.
  2. Calculate the Net Displacement:

    • Total eastward distance: km
    • Total southward distance: km
  3. Apply the Pythagorean Theorem:

    • Net displacement from the starting point is the hypotenuse of a right triangle with legs of 5 km (eastward) and 12 km (southward):

    • √(5²+12²)

    • √(25+ 144)

    • √169

    • 13km

So, the shortest aerial distance between Kabita's office and her apartment is:13 km

Answer: (B) 13 km


Importance for ADRE 2.0

  • Importance: Tests understanding of displacement and Pythagorean theorem. 
  • Enhances spatial reasoning and problem-solving skills. 
  • Crucial for competitive exam preparation, involving real-world scenarios.
  • Previously asked in ADRE 1.0 SLRC-2022 for Grade-III posts of Assam Govt. 

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