Five dancers of a dance troupe are standing on a stage facing north. Rohit is…
2026
Five dancers of a dance troupe are standing on a stage facing north. Rohit is 30 m to the right of Vikas. Somya is standing 30 m to the north of Vikas. Kaizen is standing 10 m to the left of Somya. Sanjay is standing to the south of Kaizen and left of Vikas. In what direction is Kaizen standing with respect to Rohit, and what is the shortest distance between them?
- A.
50 m, south-east
- B.
30 m, north
- C.
50 m, north-west
- D.
30 m, north-west
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Correct answer: C
Final answer: Kaizen is 50 m to the north-west of Rohit.
Place Vikas at (0, 0).
Rohit is 30 m to the right (east) of Vikas → Rohit = (30, 0).
Somya is 30 m north of Vikas → Somya = (0, 30).
Kaizen is 10 m to the left (west) of Somya → Kaizen = (0 - 10, 30) = (-10, 30).
Vector from Rohit to Kaizen = (-10 - 30, 30 - 0) = (-40, 30), i.e. 40 m west and 30 m north → direction is north-west.
Distance = sqrt(40^2 + 30^2) = sqrt(1600 + 900) = sqrt(2500) = 50 m.
Therefore, Kaizen is 50 m to the north-west of Rohit.