Direction TestsPYQ Sept 25Question 4148 of 165
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Two persons, P and Q, start walking from a meeting point towards North. After walking 100 metres, P turns left and Q turns right. P, after walking 50 metres, takes a left turn and walks 150 metres. But Q walks 30 metres, turns to his right and walks 90 metres. What is the shortest distance between P and Q now in metres?

Options

A80
B90
C100
D110
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Correct Answer

✅ Option c — 100

All Options:

  • A80
  • B90
  • C100
  • D110

Detailed Solution & Explanation

Let the meeting point be the origin (0,0)\displaystyle (0, 0). Let North be the positive y-axis, South be the negative y-axis, East be the positive x-axis, and West be the negative x-axis.
Both P and Q start by walking 100 metres North: Initial Position for both=(0,100)\text{Initial Position for both} = (0, 100)
**Path of P:** 1) From (0,100)\displaystyle (0, 100), P turns left (facing West) and walks 50 metres: PositionP1=(−50,100)\text{Position}_{P1} = (-50, 100) 2) P turns left (facing South, since he was facing West) and walks 150 metres: Final Position of P=(−50,100−150)=(−50,−50)\text{Final Position of P} = (-50, 100 - 150) = (-50, -50)
**Path of Q:** 1) From (0,100)\displaystyle (0, 100), Q turns right (facing East) and walks 30 metres: PositionQ1=(30,100)\text{Position}_{Q1} = (30, 100) 2) Q turns right (facing South, since he was facing East) and walks 90 metres: Final Position of Q=(30,100−90)=(30,10)\text{Final Position of Q} = (30, 100 - 90) = (30, 10)
Let us find the shortest distance between P (−50,−50)\displaystyle (-50, -50) and Q (30,10)\displaystyle (30, 10) using the distance formula: d=(xQ−xP)2+(yQ−yP)2d = \sqrt{\left(x_Q - x_P\right)^2 + \left(y_Q - y_P\right)^2} d=(30−(−50))2+(10−(−50))2d = \sqrt{(30 - (-50))^2 + (10 - (-50))^2} d=(30+50)2+(10+50)2d = \sqrt{(30 + 50)^2 + (10 + 50)^2} d=802+602d = \sqrt{80^2 + 60^2} d=6400+3600=10000=100 metresd = \sqrt{6400 + 3600} = \sqrt{10000} = 100\text{ metres}
Hence, **Option C** 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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