Direction TestsMCQMTP Dec 22 Series IIQuestion 2236 of 165
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Shweta moved a distance of 75m towards the north. She then turned to the left and walked about 25m, turned left again and walked 80m. Finally, she turned to the right at an angle of $45^\circ$. In which direction was she moving finally?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — South-West

All Options:

  • ASouth
  • BSouth-West
  • CNorth-East
  • DNorth-West

Detailed Solution & Explanation

Let Shweta start at the origin (0,0)\displaystyle (0, 0) facing North. Left turns correspond to counter-clockwise (+), and right turns correspond to clockwise (-).
1. **First Segment (North)**: She moves $75$ meters North. Coordinates: $P_1 = (0, 75)\displaystyle . Direction: North.<br>2. **Second Segment (Left Turn / West)**: Facing North, a left turn points West. She walks &#36;25 meters West. Coordinates: P2=(−25,75)\displaystyle P_2 = (-25, 75). Direction: West.
3. **Third Segment (Left Turn / South)**: Facing West, a left turn points South. She walks $80$ meters South. Coordinates: $P_3 = (-25, 75 - 80) = (-25, -5).Direction:South.<br>4.∗∗FinalTurn(45°Right)∗∗:FromfacingSouth(directionvector\displaystyle . Direction: South.<br>4. **Final Turn (45° Right)**: From facing South (direction vector-j^\displaystyle \hat{j}$), she turns right (clockwise, towards West $-i^<span\displaystyle \hat{i}<span class="katex-error" title="ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 20: …playstyle ) by &̲#36;45^\circ" style="color:#cc0000">\displaystyle ) by &#36;45^\circ. The resulting direction vector is:
v⃗=−sin⁡(45∘)i^−cos⁡(45∘)j^\displaystyle v⃗\displaystyle \vec{v} = -\sin(45^\circ)i^−cos⁡\displaystyle \hat{i} - \cos(45^\circ)j^\displaystyle \hat{j}
Since both the x\displaystyle x and y\displaystyle y components are negative, she is moving in the South-West direction.

Thus, she is moving in the South-West direction finally.
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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