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Circular Track

Circular Track problems involve objects moving on a circular path. Key concepts include meeting time, number of laps, and relative speed. When moving in the same direction, relative speed = difference of speeds; when moving opposite, relative speed = sum of speeds.

10Worksheets
200+Practice Questions
HardDifficulty
3-4 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Circular Track

Circular Track problems involve objects moving on a circular path. Key concepts include meeting time, number of laps, and relative speed. When moving in the same direction, relative speed = difference of speeds; when moving opposite, relative speed = sum of speeds.

Prerequisites

Relative speed concepts Circumference calculation Meeting time formula Lap completion concepts
Why This Matters: Circular Track problems appear in 1-2 questions in CAT, GMAT, and Banking PO mains exams. They test advanced relative motion concepts.

How to Solve Circular Track Problems

1

Step 1: Determine direction (same or opposite)

2

Step 2: Calculate relative speed: opposite = sum, same = difference

3

Step 3: Meeting time = Track length / Relative speed

4

Step 4: For first meeting, use track length as distance

5

Step 5: For nth meeting, multiply time by n

6

Step 6: Number of laps = Distance / Track length

Pro Strategy: For opposite directions, the runners together cover the entire track length to meet. For same direction, the faster runner must gain one full lap to meet the slower runner.

Example Problem

Example: Two runners start from same point on a 400 m track. Speeds: 8 m/s and 6 m/s. If they run in opposite directions, when will they meet first? Solution: Step 1: Opposite directions Step 2: Relative speed = 8 + 6 = 14 m/s Step 3: Track length = 400 m Step 4: Meeting time = 400 / 14 = 28.57 seconds Answer: 28.57 seconds

Pro Tips & Tricks

  • Opposite direction meeting: Time = Track length / (v₁ + v₂)
  • Same direction meeting: Time = Track length / |v₁ - v₂|
  • For nth meeting in same direction: Time = n × Track / |v₁ - v₂|
  • Number of laps completed = Distance traveled / Track length
  • Meeting points repeat every L/|v₁ - v₂| seconds

Shortcut Methods to Solve Faster

First meeting time (opposite) = L/(v₁+v₂)
First meeting time (same) = L/|v₁-v₂|
If speeds are in ratio a:b, meeting points follow pattern

Common Mistakes to Avoid

Using track length as radius instead of circumference
Forgetting to use absolute difference for same direction
Adding speeds for same direction (should subtract)
Not considering multiple meetings

Exam Importance

Circular Track is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
2-3 questions
INSURANCE
1-2 questions

Ready to Master Circular Track?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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