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Agniveer Army CEE Circular Track & Meeting

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This page covers Agniveer Army CEE Circular Track & Meeting with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Circular Track & Meeting— Rules & Concept

Core ConceptRead 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 BlockMemorise — at least one formula appears in every paper

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 PatternsWhat examiners ask — read before attempting PYQs
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 ExampleSolve this step-by-step before moving on
1
Step 1

Since they're moving in the same direction, relative speed = 10 - 6 = 4 m/s

2
Step 2

For A to meet B again, A must gain exactly one full lap = 400m

3
Step 3

Time = Distance / Speed = 400 / 4 = 100 seconds

4
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). ✓

Exam TrapsCommon mistakes students make — avoid these

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 to Remember

  • 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-Specific Tips

  • 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
Practice MCQs

Circular Track & Meeting — Practice Questions

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

Two joggers start at the same point on a circular track of 500 m and run in the same direction at speeds of 10 m/s and 6 m/s. How many times will the faster jogger lap the slower jogger in 250 seconds?

Practice 2easy

Two runners start at the same point on a circular track of length 400 m and run in the same direction. Runner A runs at 8 m/s and Runner B runs at 5 m/s. After how many seconds will Runner A lap Runner B for the first time?

Practice 3easy

Two cyclists start from opposite ends of a circular track of length 600 m and cycle towards each other at speeds of 12 m/s and 18 m/s respectively. How much time will it take for them to meet for the first time?

Practice 4medium

Two runners start together from a point on a circular track of 800 m and run in the same direction. Runner P completes one lap in 80 seconds, while Runner Q completes one lap in 100 seconds. After how many seconds will they meet at the starting point again?

Practice 5medium

Two runners start from the same point on a circular track of length 400 m and run in the same direction. Runner A runs at 8 m/s and Runner B runs at 5 m/s. After how many seconds will Runner A lap Runner B for the first time?

Practice 6medium

Two cyclists start from opposite ends of a circular track of 600 m and travel towards each other at speeds of 12 m/s and 18 m/s respectively. In how many seconds will they meet for the first time?

Practice 7medium

Three athletes start from the same point on a circular track of 500 m. They run at speeds of 10 m/s, 7 m/s, and 5 m/s respectively in the same direction. How many seconds after the start will the fastest athlete lap the slowest athlete for the first time?

Practice 8hard

Two runners start at the same point on a circular track of length 400 m. Runner A runs at 6 m/s and Runner B runs at 4 m/s in the same direction. After how many seconds will Runner A lap Runner B for the first time (i.e., be exactly 400 m ahead on the track)?

60-Second Revision — Circular Track & Meeting

  • 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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