Direction TestsMCQMTP Nov 21Question 2229 of 165
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Mamtha moved a distance of 75 m towards north, then she turns to the left and walked to about 25 m, turned left again and walks 80 m. Finally, she turns to the right at angle of 45∘\displaystyle 45^\circ. In which direction was she is moving finally?

Options

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

✅ Option b — South-West

All Options:

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

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Detailed Solution & Explanation

Let Mamtha 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\displaystyle 75 meters North. Coordinates: P1=(0,75)\displaystyle P_1 = (0, 75). Direction: North.
2. **Second Segment (Left Turn / West)**: Facing North, a left turn points West. She walks 25\displaystyle 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\displaystyle 80 meters South. Coordinates: P3=(−25,75−80)=(−25,−5)\displaystyle P_3 = (-25, 75 - 80) = (-25, -5). Direction: South.
4. **Final Turn (45° Right)**: From facing South (direction vector −j^\displaystyle -\hat{j}), she turns right (clockwise, towards West −i^\displaystyle -\hat{i}) by 45∘\displaystyle 45^\circ. The resulting direction vector is:
v⃗=−sin⁡(45∘)i^−cos⁡(45∘)j^\displaystyle \vec{v} = -\sin(45^\circ)\hat{i} - \cos(45^\circ)\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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