Direction TestsMCQMTP March 22Question 2232 of 165
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A boy from his home, first walks 20 m in North-West direction then 20 m in South - West direction. Next, he walks 20m South - East direction. Finally, he turns towards his house. In which direction is he moving?

Options

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

✅ Option b — North - East

All Options:

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

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Detailed Solution & Explanation

Let the boy's home be at the origin H(0,0)\displaystyle H(0, 0) on the Cartesian coordinate plane.
1. **First Movement (North-West)**: He walks 20\displaystyle 20 meters North-West. The vector for this movement is:
v⃗1=−2012i^+2012j^\displaystyle \vec{v}_1 = -20\frac{1}{\sqrt{2}}\hat{i} + 20\frac{1}{\sqrt{2}}\hat{j}
His coordinates become P1=(−102,102)\displaystyle P_1 = (-10\sqrt{2}, 10\sqrt{2}).
2. **Second Movement (South-West)**: From P1\displaystyle P_1, he walks 20\displaystyle 20 meters South-West. The vector for this movement is:
v⃗2=−2012i^−2012j^\displaystyle \vec{v}_2 = -20\frac{1}{\sqrt{2}}\hat{i} - 20\frac{1}{\sqrt{2}}\hat{j}
His coordinates become:
P2=P1+v⃗2=(−202,0)\displaystyle P_2 = P_1 + \vec{v}_2 = (-20\sqrt{2}, 0)
3. **Third Movement (South-East)**: From P2\displaystyle P_2, he walks 20\displaystyle 20 meters South-East. The vector for this movement is:
v⃗3=2012i^−2012j^\displaystyle \vec{v}_3 = 20\frac{1}{\sqrt{2}}\hat{i} - 20\frac{1}{\sqrt{2}}\hat{j}
His coordinates become:
P3=P2+v⃗3=(−102,−102)\displaystyle P_3 = P_2 + \vec{v}_3 = (-10\sqrt{2}, -10\sqrt{2})
4. **Final Movement (Towards Home)**: He turns and moves towards his home at H(0,0)\displaystyle H(0,0). The vector pointing from his current position P3(−102,−102)\displaystyle P_3(-10\sqrt{2}, -10\sqrt{2}) to his house H(0,0)\displaystyle H(0,0) is:
v⃗home=H−P3=102i^+102j^\displaystyle \vec{v}_{\text{home}} = H - P_3 = 10\sqrt{2}\hat{i} + 10\sqrt{2}\hat{j}
Since both components of this vector are positive, he is moving in the North-East direction.

**Note on Typographical Error**: The textbook answer key incorrectly lists Option D (South-East) as the correct answer. As mathematically proven above, to return home from his final position, the boy must move in the North-East direction. Therefore, North-East (Option B) is the mathematically correct answer.
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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