Devika started walking from a point ‘P’ and moved 210 m towards East. Then she…
2023
Devika started walking from a point ‘P’ and moved 210 m towards East. Then she turned to her right and moved 190 m, and then turned to her right and moved 400 m and again turned to her right and moved 200 m to reach a point ‘Q’. What is the direction and shortest distance of point ‘Q’ from point ‘P’?
Answer: B. West, 190 m — Concept: In a direction-and-distance walk, resolve every leg into its East–West and North–South component, add each axis separately to get the net…
- A.
West, 200 m
- B.
West, 190 m
- C.
East, 190 m
- D.
East, 200 m
Attempted by 98 students.
Show answer & explanation
Correct answer: B
Concept: In a direction-and-distance walk, resolve every leg into its East–West and North–South component, add each axis separately to get the net displacement, then apply the Pythagorean theorem for the straight-line distance; when one axis's net component is much smaller than the other, the direction of the destination is essentially along the larger axis.
Leg | Direction | Distance |
|---|---|---|
1 | East | 210 m |
2 | South | 190 m |
3 | West | 400 m |
4 | North | 200 m |
Net East–West = 400 m West − 210 m East = 190 m West.
Net North–South = 200 m North − 190 m South = 10 m North.
The 10 m North component is small next to the 190 m West component, so the overall direction of Q from P is essentially West.
Straight-line distance PQ = √(1902 + 102) ≈ 190.26 m, which rounds to the 190 m offered among the choices.
Cross-check with signed coordinates: taking East and North as positive, the four legs give (+210, 0), (0, −190), (−400, 0), (0, +200); summing gives (210−400, −190+200) = (−190, +10) — the same net position 190 m west and 10 m north of P, confirming the result independently.
Note: the question asks the direction of Q from P (i.e., where Q lies as seen from P) — not the return direction from Q to P. Since P is roughly 190 m east of Q, Q lies to the west of P; only the reverse trip (Q to P) would point east.
Conclusion: West, 190 m is the direction and shortest distance of Q from P among the given choices.