Direction TestsPYQ May 25Question 4348 of 165
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Two cars start from the opposite places on a highway, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the meantime, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?

Options

A65 km.
B75 km.
C80 km.
D85 km.
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Correct Answer

Option a65 km.

All Options:

  • A65 km.
  • B75 km.
  • C80 km.
  • D85 km.

Detailed Solution & Explanation

Let the highway (main road) be represented by the x-axis (y=0\displaystyle y = 0).
Let the starting point of the first car be (0,0)\displaystyle (0, 0) and the starting point of the second car be (150,0)\displaystyle (150, 0), so they are 150\displaystyle 150 km apart.
- First car starts at (0,0)\displaystyle (0,0) and heads east (+x\displaystyle +x direction).
- Second car starts at (150,0)\displaystyle (150,0) and heads west (x\displaystyle -x direction).

Let\'s trace the path of the first car:
1. Runs 25\displaystyle 25 km along the highway: reaches (25,0)\displaystyle (25, 0).
2. Takes a right turn (facing South, y\displaystyle -y direction) and runs 15\displaystyle 15 km: reaches (25,15)\displaystyle (25, -15).
3. Turns left (facing East, +x\displaystyle +x direction) and runs 25\displaystyle 25 km: reaches (25+25,15)=(50,15)\displaystyle (25 + 25, -15) = (50, -15).
4. Takes the direction back to reach the main road (y=0\displaystyle y = 0). This means it moves North (+y\displaystyle +y direction) for 15\displaystyle 15 km. Its position on the highway is now (50,0)\displaystyle (50, 0).

Let\'s trace the path of the second car:
1. Moves only along the main road (x\displaystyle -x direction) for 35\displaystyle 35 km.
2. Its position is (15035,0)=(115,0)\displaystyle (150 - 35, 0) = (115, 0).

Now, both cars are back on the main road (y=0\displaystyle y = 0):
- Position of First Car: (50,0)\displaystyle (50, 0)
- Position of Second Car: (115,0)\displaystyle (115, 0)
The distance between the two cars is:
Distance=11550=65 km\text{Distance} = 115 - 50 = 65 \text{ km}
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.

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This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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