Eight persons M through T are standing in such a way that O is 20 m apart from…
2025
Eight persons M through T are standing in such a way that O is 20 m apart from N towards West, N is 30 m South with respect to M. M is 40 m towards West with respect to Q. P is 50 m towards South with respect to Q. R is 15 m apart from S towards North. T is 20 m towards East with respect to S. R is 40 m towards West with respect to P. What is the direction of O with respect to S?
Answer: A. North-West — ConceptIn direction-sense problems, assign coordinates to one reference point and translate each relation into a displacement. East and West change the…
- A.
North-West
- B.
North
- C.
West
- D.
Cannot be determined
Attempted by 9 students.
Show answer & explanation
Correct answer: A
Concept
In direction-sense problems, assign coordinates to one reference point and translate each relation into a displacement. East and West change the horizontal coordinate; North and South change the vertical coordinate.
A point is north-west of another when its horizontal displacement is negative and its vertical displacement is positive.
Application
Take S as (0, 0). Since R is 15 m north of S, R = (0, 15).
R is 40 m west of P, so P is 40 m east of R: P = (40, 15).
P is 50 m south of Q, so Q is 50 m north of P: Q = (40, 65).
M is 40 m west of Q, giving M = (0, 65).
N is 30 m south of M, giving N = (0, 35).
O is 20 m west of N, giving O = (-20, 35).
Cross-check
Relative to S = (0, 0), O has displacement (-20, 35): the horizontal component is westward and the vertical component is northward. The independent sign check therefore gives North-West.
Result: O is North-West of S.