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NIACL AO Circular Track & Meeting

Study Material — 4 PYQs (2018–2020) · Concept Notes · Shortcuts

NIACL AO Circular Track & Meeting is a frequently tested subtopic — 4 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

NIACL AO Circular Track & Meeting — Past Exam Questions

4 questions from actual NIACL AO papers · all shown free · click option to reveal solution

Exam Q 12019Previous Year Pattern

Two runners, A and B, start running simultaneously from the same point on a circular track of length 400 metres. A runs at 8 m/s and B runs at 6 m/s in the same direction. After how many seconds will A lap B for the first time (i.e., A will be exactly one full lap ahead of B)?

Exam Q 22020Previous Year Pattern

Two runners, A and B, start running simultaneously from the same point on a circular track of length 400 metres. A runs at 8 m/s and B runs at 6 m/s in the same direction. After how many seconds will A lap B for the first time (i.e., A will be exactly 400 metres ahead of B)?

Exam Q 32020Previous Year Pattern

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

Exam Q 42018Previous Year Pattern

A circular track has a circumference of 1200 m. Three runners A, B, and C start from the same point at the same time in the same direction with speeds 4 m/s, 6 m/s, and 10 m/s respectively. After how many seconds will all three meet together for the FIRST time at the starting point?

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

47graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 47

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Practice 1easy

Runners X and Y start together from a point on a circular track of 1200 m. X runs at 9 m/s and Y runs at 6 m/s in the same direction. What is the distance covered by Y when X laps Y for the first time?

Practice 2easy

Two joggers P and Q start from the same point on a circular track of 800 m and run in opposite directions at 6 m/s and 4 m/s respectively. After how many seconds will they meet for the second time?

Practice 3easy

On a circular track of 1200 metres, Runner M and Runner N start together from the same point and run in the same direction. M runs at 15 m/s and N runs at 9 m/s. What is the distance covered by N when M laps N for the first time?

Practice 4easy

Two cyclists start simultaneously from opposite ends of a circular track of circumference 600 metres. They cycle 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 5easy

Two runners, A and B, start from the same point on a circular track of length 400 metres. A runs at 8 m/s and B runs at 6 m/s in the same direction. After how many seconds will A lap B (i.e., be exactly one full lap ahead)?

Practice 6easy

Two cyclists start from opposite ends of a circular track of circumference 600 metres and cycle towards each other. Cyclist X cycles at 10 m/s and Cyclist Y cycles at 5 m/s. In how many seconds will they meet for the first time?

Practice 7easy

Two joggers start from the same point on a circular track of length 300 metres. Jogger X runs at 6 m/s and Jogger Y runs at 4 m/s, both in the same direction. How many seconds after the start will X be exactly 150 metres ahead of Y on the track?

Practice 8easy

Two cyclists start simultaneously from opposite ends of a circular track of circumference 500 m, running towards each other at speeds of 10 m/s and 15 m/s respectively. In how many seconds will they meet for the first time?

Practice 9easy

A and B run on a circular track of 500 metres. A completes one lap in 50 seconds, while B completes one lap in 100 seconds. If they start together from the same point and run in the same direction, how many times will A lap B in 500 seconds?

Practice 10easy

A and B run on a circular track of 500 metres. A completes one lap in 50 seconds, while B completes one lap in 100 seconds. If they start together from the same point in the same direction, how many times will A overtake B in 500 seconds?

Practice 11easy

Two runners, A and B, start running on a circular track of length 400 metres from the same point in the same direction. A runs at 8 m/s and B runs at 6 m/s. After how many seconds will A lap B (i.e., be exactly one full lap ahead)?

Practice 12easy

Two persons P and Q start from the same point on a circular track of circumference 800 metres and run in opposite directions. P runs at 12 m/s and Q runs at 8 m/s. How many seconds after the start will they meet for the second time?

Practice 13easy

Two athletes start from the same point on a circular track of 360 metres and run in the same direction. Athlete A runs at 6 m/s and Athlete B runs at 4 m/s. After how many seconds will they be at the same point on the track for the second time (including the start)?

Practice 14easy

Two athletes start from the same point on a circular track of 300 metres and run in the same direction. The first athlete runs at 6 m/s and the second at 4 m/s. After the first athlete completes 10 laps, how many complete laps will the second athlete have completed?

Practice 15easy

Two cyclists start from the same point on a circular track of circumference 600 metres and cycle in opposite directions. Their speeds are 12 m/s and 8 m/s respectively. After how many seconds will they meet for the first time?

Practice 16easy

Two runners, A and B, start running on a circular track of length 400 metres at the same time from the same point. A runs at 8 m/s and B runs at 6 m/s in the same direction. After how many seconds will A lap B (i.e., be exactly one full lap ahead)?

Practice 17easy

A and B run on a circular track of 600 m. A runs at 12 m/s and B runs at 8 m/s in the same direction. How many times will A lap B in 10 minutes?

Practice 18easy

Two athletes A and B run on a circular track of 500 m starting from the same point at the same time. A runs at 10 m/s and B runs at 7 m/s in the same direction. How many complete laps will B have run when A completes 5 laps?

Practice 19medium

Two cyclists start from opposite ends of a circular track of 600 metres and cycle towards each other. The first cyclist travels at 12 m/s and the second at 8 m/s. How many seconds will it take for them to meet for the second time?

Practice 20medium

A and B run on a circular track of 500 m. A runs at 10 m/s and B runs at 6 m/s in the same direction. If they start together, after how many seconds will they be at the same point again for the second time?

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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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