Direction TestsMCQPYQ June 19Question 2201 of 165
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Sangeeta leaves from her home. She first walks 30 meters in north-west direction and then 30m in south-west direction, next she walks 30 meters in south-east direction. Finally she turns towards her house. In which direction is she moving now.

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

✅ Option a — North - East

All Options:

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

Detailed Solution & Explanation

Let Sangeeta's home be at the origin H(0,0)\displaystyle H(0, 0) on the Cartesian plane, where the positive y\displaystyle y-axis represents North, the negative y\displaystyle y-axis represents South, the positive x\displaystyle x-axis represents East, and the negative x\displaystyle x-axis represents West.
1. **First Movement (North-West)**: She walks $30metersNorth−West.Thevectorforthismovementis:<br>\displaystyle meters North-West. The vector for this movement is:<br>v⃗1=30\displaystyle \vec{v}_1 = 30 \cos(135^\circ)i^+30\displaystyle \hat{i} + 30 \sin(135^\circ)j^\displaystyle \hat{j} = -3012\displaystyle \frac{1}{\sqrt{2}}i^+30\displaystyle \hat{i} + 3012\displaystyle \frac{1}{\sqrt{2}}j^\displaystyle \hat{j} ≈−21\displaystyle \approx -21.21i^+21\displaystyle \hat{i} + 21.21j^<span\displaystyle \hat{j}<span class="katex"><br>Herpositionbecomes\displaystyle <br>Her position becomesP_1 = (-152\displaystyle \sqrt{2}, 152\displaystyle \sqrt{2}).<br>2.∗∗SecondMovement(South−West)∗∗:From\displaystyle .<br>2. **Second Movement (South-West)**: FromP_1$, she walks $30$ meters South-West. The vector for this movement is:
v⃗2=30cos⁡(225∘)i^+30sin⁡(225∘)j^=−3012i^−3012j^≈−21.21i^−21.21j^\displaystyle v⃗2=30\displaystyle \vec{v}_2 = 30 \cos(225^\circ)i^+30\displaystyle \hat{i} + 30 \sin(225^\circ)j^\displaystyle \hat{j} = -3012\displaystyle \frac{1}{\sqrt{2}}i^−30\displaystyle \hat{i} - 3012\displaystyle \frac{1}{\sqrt{2}}j^\displaystyle \hat{j} ≈−21\displaystyle \approx -21.21i^−21\displaystyle \hat{i} - 21.21j^\displaystyle \hat{j}
Her new position is:
P2=P1+v⃗2=(−152−152,152−152)=(−302,0)≈(−42.43,0)\displaystyle P_2 = P_1 + v⃗2\displaystyle \vec{v}_2 = (-152−15\displaystyle \sqrt{2} - 152\displaystyle \sqrt{2}, 152−15\displaystyle \sqrt{2} - 152\displaystyle \sqrt{2}) = (-302\displaystyle \sqrt{2}, 0) ≈\displaystyle \approx (-42.43, 0)
3. **Third Movement (South-East)**: From P2\displaystyle P_2, she walks $30metersSouth−East.Thevectorforthismovementis:<br>\displaystyle meters South-East. The vector for this movement is:<br>v⃗3=30\displaystyle \vec{v}_3 = 30 \cos(315^\circ)i^+30\displaystyle \hat{i} + 30 \sin(315^\circ)j^=30\displaystyle \hat{j} = 3012\displaystyle \frac{1}{\sqrt{2}}i^−30\displaystyle \hat{i} - 3012\displaystyle \frac{1}{\sqrt{2}}j^\displaystyle \hat{j} ≈\displaystyle \approx 21.21i^−21\displaystyle \hat{i} - 21.21j^<span\displaystyle \hat{j}<span class="katex"><br>Hernewpositionis:<br>\displaystyle <br>Her new position is:<br>P_3 = P_2 + v⃗3\displaystyle \vec{v}_3 = (-302+15\displaystyle \sqrt{2} + 152\displaystyle \sqrt{2}, 0 - 152\displaystyle \sqrt{2}) = (-152\displaystyle \sqrt{2}, -152\displaystyle \sqrt{2}) ≈\displaystyle \approx (-21.21, -21.21)<br>4.∗∗FinalMovement(TowardsHome)∗∗:Sangeetanowturnsandmovestowardsherhomeat\displaystyle <br>4. **Final Movement (Towards Home)**: Sangeeta now turns and moves towards her home atH(0,0)$. The vector pointing from her current position $P_3(-152\displaystyle \sqrt{2}, -152\displaystyle \sqrt{2})$ to her house $H(0,0)is:<br>\displaystyle is:<br>v⃗\displaystyle \vec{v}_{home\displaystyle \text{home}} = H - P_3 = (0 - (-152\displaystyle \sqrt{2}))i^\displaystyle \hat{i} + (0 - (-152\displaystyle \sqrt{2}))j^=15\displaystyle \hat{j} = 152\displaystyle \sqrt{2}i^+15\displaystyle \hat{i} + 152\displaystyle \sqrt{2}j^<span\displaystyle \hat{j}<span class="katex"><br>Sinceboththe\displaystyle <br>Since both thexand\displaystyle andy$ components of this direction vector are positive, she is moving in the North-East direction.

**Note on Typographical Error**: The textbook answer key lists Option B (North-West) as correct, which is a typographical error. As mathematically shown above, she must travel in the North-East direction to reach her home from her final position. Therefore, North-East (Option A) is the mathematically correct answer.
Hence, **Option A** 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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