A lady while going to her college in a car drove 20 kms towards north and then 15 kms towards west. She then turned to the south and covered 10 kms. Further she turned to the east and moved 12 kms. Finally she turned right and drove 10 kms. How far and in which direction is the lady from her starting point ?
3 km, West
Concept: Track movement on a coordinate grid: East is +x, West is −x, North is +y, South is −y. The straight-line distance and direction from the start are read from the final coordinates.
Step-by-step working: Start at (0, 0).
1. North 20 km → (0, 20).
2. West 15 km → (−15, 20).
3. South 10 km → (−15, 10).
4. East 12 km → (−3, 10).
5. Now facing East, she turns right → she now faces South; drive 10 km → (−3, 0).
Final position = (−3, 0).
Since y = 0 (same north–south level as start) and x = −3, she is 3 km to the west of the start.
Distance = 3 km, direction = West.
Why the other choices are wrong:
- 5 km South is wrong: the net north–south displacement cancels to 0, so she is neither north nor south of the start.
- 5 km West is wrong: the net westward displacement is 15 − 12 = 3 km, not 5 km.
- 3 km North is wrong: her final y-coordinate is 0, so there is no northward gap.
Only 3 km West matches the final coordinates.
Takeaway: Convert each leg into x/y steps and read off the resultant.
Correct answer: 3 km, West
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
