Two brothers Abhishek (A) and Bandhan (B) start running from a common point.…
2023
Two brothers Abhishek (A) and Bandhan (B) start running from a common point. Abhishek goes 20 km towards North-East whereas Bandhan goes 16 km towards East and then 12 km towards North. How far are A and B from each other?
- A.
64 km
- B.
27 km
- C.
81 km
- D.
None
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Solution:
Find components of Abhishek's displacement (20 km North‑East): east = 20·cos45° = 10√2 ≈ 14.14 km, north = 10√2 ≈ 14.14 km.
Find components of Bandhan's displacement (16 km east then 12 km north): east = 16 km, north = 12 km.
Compute difference vector (Abhishek − Bandhan): Δx = 10√2 − 16 ≈ −1.86 km, Δy = 10√2 − 12 ≈ 2.14 km.
Distance between them = √(Δx² + Δy²) ≈ √( (−1.86)² + (2.14)² ) ≈ √(8.04) ≈ 2.84 km.
Conclusion: The correct separation is about 2.84 km, so none of the numeric choices (64 km, 27 km, 81 km) is correct; therefore the 'None' choice is correct.