Direction TestsMCQMTP Oct 21Question 2231 of 165
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A man is facing south. He turns 135\displaystyle 135^\circ in the anticlockwise direction and then 180\displaystyle 180^\circ in the clockwise direction. Which direction is he facing now?

Options

ANorth-East
BNorth-West
CSouth-East
DSouth-West
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Correct Answer

Option dSouth-West

All Options:

  • ANorth-East
  • BNorth-West
  • CSouth-East
  • 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 South, which corresponds to an angle of 270\displaystyle 270^\circ.
2. **First Rotation**: Turns 135\displaystyle 135^\circ in the anticlockwise direction:
Angle1=270+135=40545(North-East)\displaystyle \text{Angle}_1 = 270^\circ + 135^\circ = 405^\circ \equiv 45^\circ \quad (\text{North-East})
3. **Second Rotation**: Turns 180\displaystyle 180^\circ in the clockwise direction:
Angle2=45180=135225\displaystyle \text{Angle}_2 = 45^\circ - 180^\circ = -135^\circ \equiv 225^\circ

An angle of 225\displaystyle 225^\circ lies in the third quadrant (between West at 180\displaystyle 180^\circ and South at 270\displaystyle 270^\circ), which corresponds to the South-West direction. (Note that a 180\displaystyle 180^\circ turn always points to the exact opposite direction, and the opposite of North-East is South-West).

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