Direction TestsMCQMTP May 20Question 2222 of 165
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A man is facing towards East and turns through 45\displaystyle 45^\circ clockwise again 180\displaystyle 180^\circ clock-wise and then turns through 270\displaystyle 270^\circ anti-clock wise. In which direction is he facing now?

Options

ANorth
BNorth-East
CSouth
DSouth-West
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Correct Answer

Option bNorth-East

All Options:

  • ANorth
  • BNorth-East
  • CSouth
  • DSouth-West

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Detailed Solution & Explanation

Let's represent the directions using standard angles where East is 0\displaystyle 0^\circ, North is 90\displaystyle 90^\circ, West is 180\displaystyle 180^\circ, and South is 270\displaystyle 270^\circ. Clockwise rotation corresponds to subtracting angles, and counter-clockwise (anticlockwise) rotation corresponds to adding angles.
1. **Initial State**: Facing East, which corresponds to an angle of 0\displaystyle 0^\circ.
2. **First Rotation**: Turns 45\displaystyle 45^\circ in the clockwise direction:
Angle1=045=45\displaystyle \text{Angle}_1 = 0^\circ - 45^\circ = -45^\circ
3. **Second Rotation**: Turns 180\displaystyle 180^\circ in the clockwise direction:
Angle2=45180=225\displaystyle \text{Angle}_2 = -45^\circ - 180^\circ = -225^\circ
4. **Third Rotation**: Turns 270\displaystyle 270^\circ in the anticlockwise direction:
Angle3=225+270=45\displaystyle \text{Angle}_3 = -225^\circ + 270^\circ = 45^\circ

An angle of 45\displaystyle 45^\circ lies in the first quadrant, exactly halfway between East (0\displaystyle 0^\circ) and North (90\displaystyle 90^\circ). This corresponds to the North-East direction.

**Note on Typographical Error**: The textbook answer key incorrectly lists Option C (South) as the correct answer. As mathematically and geometrically proven above, the man is facing North-East. Therefore, North-East (Option B) is the correct answer.
Hence, **Option B** 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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