Question

Miss Lilly' started her journey from her house and goes 2 km straight. Then, she turns towards her right and goes 1 km. She again turns towards her right and goes 1 km again. If finally she is in the north-west direction from her house, then in which direction did she go in the beginning ?

• A. North
• B. South
• C. East
• D. West

Answer 1

The Correct Option is D

To solve the problem, we need to map out Miss Lilly's journey and determine the initial direction she took.

1. Miss Lilly starts her journey from her house and travels 2 km straight in an unknown initial direction. Let's denote this initial direction as X.
2. She then turns to her right and travels 1 km. Turning right depends on the initial direction:
   • If she was going North, she will turn East.
   • If she was going South, she will turn West.
   • If she was going East, she will turn South.
   • If she was going West, she will turn North.
3. Again, she turns right and travels 1 km. Similarly:
   • If she was going East, turning right means heading South.
   • If she was going West, turning right means heading North.
   • If she was going South, turning right means heading West.
   • If she was going North, turning right means heading East.
4. We are informed that, finally, she is in the north-west direction from her house. This final position helps us determine her initial direction.

Using the last clue that her final position is to the north-west of her starting point, we can deduce the following:

• If the initial direction X was West, she would first travel 2 km west, then 1 km north after the two right turns, consistent with ending up north-west.
• Other initial directions (North, South, East) would not result in a north-west final position.

Therefore, the initial direction Miss Lilly took was West.