Direction TestsMCQMTP Nov 21Question 2228 of 165
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Sanjay started from his house towards West. After walking a distance 15 km he turned to the right and walked 10 km, he again turned to the right and walked 5 km. After this he turns left at 135∘\displaystyle 135^\circ and covered 10 km in which direction should he is going?

Options

ASouth
BSouth-West
CSouth-East
DNorth-West
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Correct Answer

✅ Option d — North-West

All Options:

  • ASouth
  • BSouth-West
  • CSouth-East
  • DNorth-West

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Detailed Solution & Explanation

Let's represent directions on a Cartesian coordinate plane with the starting point at the origin (0,0)\displaystyle (0, 0). 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. Left turns correspond to counter-clockwise (+), and right turns correspond to clockwise (-).
1. **Initial Segment (West)**: Sanjay walks 15 km\displaystyle 15\text{ km} towards the West. Coordinates: (−15,0)\displaystyle (-15, 0). Direction: West (180∘\displaystyle 180^\circ).
2. **Second Segment (Right Turn / North)**: He turns right (90∘\displaystyle 90^\circ clockwise turn from West points North) and walks 10 km\displaystyle 10\text{ km}. Coordinates: (−15,10)\displaystyle (-15, 10). Direction: North (90∘\displaystyle 90^\circ).
3. **Third Segment (Right Turn / East)**: He turns right again (90∘\displaystyle 90^\circ clockwise turn from North points East) and walks 5 km\displaystyle 5\text{ km}. Coordinates: (−15+5,10)=(−10,10)\displaystyle (-15 + 5, 10) = (-10, 10). Direction: East (0∘\displaystyle 0^\circ).
4. **Final Turn (135° Left)**: From East (0∘\displaystyle 0^\circ), he turns left (counter-clockwise) by 135∘\displaystyle 135^\circ. The new direction is:
Angle=0∘+135∘=135∘\displaystyle \text{Angle} = 0^\circ + 135^\circ = 135^\circ
Since 135∘\displaystyle 135^\circ lies in the second quadrant (between North at 90∘\displaystyle 90^\circ and West at 180∘\displaystyle 180^\circ), he is going in the North-West direction.

**Note on Typographical Error**: The textbook answer key lists Option B (South-West) as correct, which is a typographical error. As mathematically and geometrically proven above, a 135∘\displaystyle 135^\circ left turn from the East direction must point to North-West. Therefore, North-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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At a crossing, there was a direction pole, which was showing all the four correct directions. But due to the wind, it turns in such a manner that now West pointer is showing South. Harish went in the wrong direction thinking that he was travelling East. In which direction he was actually travelling?

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