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Circular Track & Meeting

LIC ADO · Quantitative Aptitude

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Core Concept

Read this first — the foundation of the topic

CIRCULAR TRACK & MEETING PROBLEMS CORE CONCEPT When two or more people move on a circular track, they start from the same point and move in the same or opposite directions. We need to find when they meet again, how many times they meet, or their relative speeds. This is different from linear track problems because the track repeats — people can meet multiple times at different points. KEY RULES & PROPERTIES 1. Same Direction Meeting: Person A and B start together.

A is faster. A will lap (overtake) B when A covers exactly one full lap MORE than B. They meet again when the faster person gains a full circle's distance on the slower one. 2. Opposite Direction Meeting: They are moving towards each other.

They meet every time their combined distance equals the track length. 3. Relative Speed Concept: In same direction, relative speed = (Speed of faster person) - (Speed of slower person). In opposite direction, relative speed = (Speed of person 1) + (Speed of person 2). 4. Time Between Meetings: This stays constant for each meeting if speeds are constant. FORMULA BLOCK Same direction (A catches B): • Time to meet = Track Length / (Speed of A - Speed of B) • In n meetings, faster person covers n × Track Length more than slower person Opposite direction: • Time to first meeting = Track Length / (Speed A + Speed B) • They meet again at same time intervals after the first meeting EXAM PATTERNS 1. Two persons on circular track, find when they meet next 2.

How many times do they meet in a given time? 3. At what point on the track do they meet? 4. Relative speed and time calculation problems SHORTCUT/TRICK "For same direction problems: Just find how long it takes for the faster person to gain one full lap.

That's your meeting time. Multiply by the number you need." WORKED EXAMPLE A and B run on a 400m circular track. A's speed is 10 m/s and B's speed is 6 m/s.

Both start together from the same point in the same direction. When will they meet again? Step 1: Since they're moving in the same direction, relative speed = 10 - 6 = 4 m/s Step 2: For A to meet B again, A must gain exactly one full lap = 400m Step 3: Time = Distance / Speed = 400 / 4 = 100 seconds Step 4: They meet again after 100 seconds. Verification: In 100 seconds, A covers = 10 × 100 = 1000m = 2 full laps + 200m. B covers = 6 × 100 = 600m = 1 full lap + 200m.

Both are at the same point (200m mark). ✓ COMMON MISTAKE Students often forget that in SAME direction, you subtract speeds. They wrongly add speeds (which is for opposite direction only). This leads to completely wrong answers.

Always check the direction first.

🔑 Key Points

Same direction: Relative speed = Speed₁ - Speed₂; opposite direction: Relative speed = Speed₁ + Speed₂
Meeting time in same direction = Track Length ÷ (Speed difference)
In opposite directions, they meet every Track Length ÷ (Sum of speeds) seconds
For the first meeting in same direction, find when the faster person gains exactly one full lap
Number of meetings in time T = T ÷ (Time between consecutive meetings)
Always identify the direction of motion FIRST before selecting your formula

📌 Exam Facts

In same-direction circular motion, the faster runner meets the slower runner when the difference in distances covered equals the track length
Meeting time formula for same direction: t = L/(v₁ - v₂) where L is track length and v₁, v₂ are speeds
In opposite-direction circular motion on a track, the first meeting occurs at time t = L/(v₁ + v₂)
When two people meet on a circular track moving in opposite directions, subsequent meetings occur at equal time intervals of L/(v₁ + v₂)
For same-direction motion, if person A is faster and they start together, A will lap B (meet again) based on relative speed only, not absolute speeds
The meeting point on a circular track can be found by calculating distance covered by either person in the time interval until meeting
In circular track problems, number of meetings in time T = T × (v₁ + v₂) / L for opposite direction motion

🚀 60-Second Revision

Formula Check: Same direction = subtract speeds; opposite direction = add speeds. Wrong operator = wrong answer.
Remember: In same direction, meeting time = Track Length ÷ (Speed difference). This is your key formula.
Trap: Don't confuse 'when they meet' with 'meeting point on track' — calculate time first, then find position if needed.
Opposite direction shortcut: They meet every T seconds where T = Track Length ÷ (v₁ + v₂).
Verification step: Always check your answer makes sense — faster person should cover more distance in same time.
For 'how many times' questions: Count = Total Time ÷ Time between each meeting.

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