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SBI PO Circular Track & Meeting

Study Material — 16 PYQs (2022–2022) · Concept Notes · Shortcuts

SBI PO Circular Track & Meeting is a frequently tested subtopic — 16 previous year questions from 2022–2022 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SBI PO Circular Track & Meeting — Past Exam Questions

16 questions from actual SBI PO papers · all shown free · click option to reveal solution

Exam Q 12022Previous Year Pattern

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 for the first time?

Exam Q 22022Previous Year Pattern

Two athletes P and Q run on a circular track of 400 metres. P runs at 12 m/s and Q runs at 8 m/s, both starting from the same point in the same direction. What is the time interval between their first and second meetings?

Exam Q 32022Previous Year Pattern

Two cyclists start from opposite ends of a circular track of 600 metres and cycle 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?

Exam Q 42022Previous Year Pattern

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?

Exam Q 52022Previous Year Pattern

Two joggers start from the same point on a circular track of 800 metres and jog in opposite directions at 6 m/s and 4 m/s respectively. How many seconds after the start will they meet for the second time?

Exam Q 62022Previous Year Pattern

On a circular track of 1200 metres, runner X takes 120 seconds to complete one lap while runner Y takes 150 seconds. Starting together from the same point in the same direction, after how many seconds will X be exactly 2 laps ahead of Y?

Exam Q 72022Previous 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 first time?

Exam Q 82022Previous Year Pattern

Two cyclists start from opposite ends of a circular track of circumference 600 metres at the same time. They cycle towards each other at speeds of 12 m/s and 8 m/s respectively. How many times will they meet in the first 5 minutes?

Exam Q 92022Previous Year Pattern

Two joggers start from the same point on a circular track of length 800 metres. Jogger X runs at 6 m/s and Jogger Y runs at 4 m/s in the same direction. How many times will X lap Y in 20 minutes?

Exam Q 102022Previous Year Pattern

On a circular track of 1200 metres, two runners P and Q start from the same point. P runs at 15 m/s and Q runs at 9 m/s in the same direction. At what time will P and Q meet for the second time?

Exam Q 112022Previous Year Pattern

Two athletes start from opposite ends of a circular track of circumference 1000 metres and run towards each other. Athlete M runs at 10 m/s and Athlete N runs at 15 m/s. If they start at the same time, in how many seconds will they meet for the third time?

Exam Q 122022Previous Year Pattern

Two cyclists start from opposite ends of a circular track of circumference 600 metres at the same time. Cyclist X travels at 12 m/s and Cyclist Y travels at 8 m/s. They meet for the second time after how many seconds?

Exam Q 132022Previous Year Pattern

On a circular track of 500 metres, Runner P starts from point A and runs at 10 m/s, while Runner Q starts from point A at the same time and runs at 6 m/s in the same direction. After P completes exactly 5 full laps, how many complete laps will Q have completed?

Exam Q 142022Previous Year Pattern

Two athletes, M and N, run on a circular track of 800 metres. M runs at 16 m/s and N runs at 12 m/s, both starting from the same point in the same direction. How many times will M lap N in 20 minutes?

Exam Q 152022Previous Year Pattern

On a circular track, Racer A and Racer B start from the same point. A runs at 15 m/s and B runs at 9 m/s in the same direction. The track length is such that A completes one lap in 60 seconds. After how many seconds will A and B meet again at the starting point simultaneously?

Exam Q 162022Previous Year Pattern

Two joggers, X and Y, start from opposite ends of a circular track of 1200 metres. X jogs at 8 m/s and Y jogs at 10 m/s towards each other. After their first meeting, they continue jogging. At what distance from X's starting point will they meet for the third time?

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

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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