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Rajni walked 20 m towards the North. Then she turned right and walks 30 m. Then she turns right and walks 35 m. Then she turns left and walks 15 m. Finally she turns left and walks 15 m. In which direction and how many meters is she from the starting position?

Options

A15 m West
B30 m East
C30 m West
D45 m East
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Correct Answer

✅ Option d — 45 m East

All Options:

  • A15 m West
  • B30 m East
  • C30 m West
  • D45 m East

Detailed Solution & Explanation

Let the starting point of Rajni be the origin (0,0)\displaystyle (0, 0) in a standard Cartesian coordinate system, where:
- +y\displaystyle +y direction represents North
- −y\displaystyle -y direction represents South
- +x\displaystyle +x direction represents East
- −x\displaystyle -x direction represents West

Let\'s trace Rajni\'s movements step-by-step:
1. **Walks 20 m North**:
New position: (0,20)\displaystyle (0, 20)
2. **Turns right and walks 30 m**:
Turning right from North means facing East (+x\displaystyle +x direction).
New position: (0+30,20)=(30,20)\displaystyle (0 + 30, 20) = (30, 20)
3. **Turns right and walks 35 m**:
Turning right from East means facing South (−y\displaystyle -y direction).
New position: (30,20−35)=(30,−15)\displaystyle (30, 20 - 35) = (30, -15)
4. **Turns left and walks 15 m**:
Turning left from South means facing East (+x\displaystyle +x direction).
New position: (30+15,−15)=(45,−15)\displaystyle (30 + 15, -15) = (45, -15)
5. **Finally turns left and walks 15 m**:
Turning left from East means facing North (+y\displaystyle +y direction).
New position: (45,−15+15)=(45,0)\displaystyle (45, -15 + 15) = (45, 0)

The final position is (45,0)\displaystyle (45, 0). The distance from the starting position (0,0)\displaystyle (0, 0) is 45\displaystyle 45 m, and the direction is along the positive x-axis, which is East. Therefore, she is 45 m East from the starting point.
Hence, **Option D** is the correct answer.

About This Chapter: Direction Tests

Paper

Paper 3: Quantitative Aptitude

Weightage

5 Marks

Key Topics

Direction Sense Test

This chapter covers Direction Sense Test and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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