Question 1

Two friends start jogging on a circular track of 800 m from the same point. Friend X jogs at 6 m/s and Friend Y jogs at 4 m/s in the same direction. How many times will X lap Y in 20 minutes?

Accepted Answer

Step 1: Convert 20 minutes to seconds: 20 × 60 = 1200 seconds. Step 2: Relative speed = 6 − 4 = 2 m/s. Step 3: Distance gained by X in 1200 seconds = 2 × 1200 = 2400 m. Step 4: Number of laps = 2400 ÷ 800 = 3 times.

Question 2

Two athletes run on a circular track of 400 m. Athlete A runs at 10 m/s and Athlete B runs at 6 m/s in the same direction, starting from the same point at the same time. After A completes 5 full laps, how many complete laps will B have completed?

Accepted Answer

Step 1: Time for A to complete 5 laps = (5 × 400) ÷ 10 = 2000 ÷ 10 = 200 seconds. Step 2: In 200 seconds, distance covered by B = 6 × 200 = 1200 m. Step 3: Number of laps by B = 1200 ÷ 400 = 3 complete laps.

Question 3

On a circular track of 1200 m, two runners start together from the same point. Runner P completes the track in 60 seconds, and Runner Q completes it in 80 seconds. Both run in the same direction. At what time will they meet again at the starting point?

Accepted Answer

Step 1: P's speed = 1200 ÷ 60 = 20 m/s. Q's speed = 1200 ÷ 80 = 15 m/s. Step 2: P completes one lap in 60 seconds, Q in 80 seconds. Step 3: They meet at the starting point when the time is a common multiple of their lap times. Step 4: LCM(60, 80) = 240 seconds.

Question 4

Two runners, A and B, start running on a circular track of length 400 m 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?

Accepted Answer

Step 1: For A to lap B, A must gain one complete lap (400 m) on B. Step 2: Relative speed = 8 − 6 = 2 m/s. Step 3: Time = Distance ÷ Relative speed = 400 ÷ 2 = 200 seconds.

Question 5

Two cyclists start from the same point on a circular track of circumference 600 m and travel in opposite directions. The first cyclist travels at 12 m/s and the second at 18 m/s. How many seconds will it take for them to meet for the first time?

Accepted Answer

Step 1: When moving in opposite directions on a circular track, they approach each other. Step 2: Relative speed = 12 + 18 = 30 m/s. Step 3: Time to meet = Track length ÷ Relative speed = 600 ÷ 30 = 20 seconds.

Question 6

A and B run on a circular track of 500 m. 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, after how many seconds will A be exactly 2 laps ahead of B?

Accepted Answer

Step 1: A's speed = 500 ÷ 50 = 10 m/s. B's speed = 500 ÷ 100 = 5 m/s. Step 2: For A to be 2 laps ahead, A must gain 2 × 500 = 1000 m on B. Step 3: Relative speed = 10 − 5 = 5 m/s. Step 4: Time = 1000 ÷ 5 = 200 seconds.

Question 7

Two runners start from the same point on a circular track of 600 m. Runner M runs at 12 m/s and Runner N runs at 8 m/s in opposite directions. How many times will they meet in 3 minutes?

Accepted Answer

Step 1: When running in opposite directions, relative speed = 12 + 8 = 20 m/s. Step 2: Time = 3 minutes = 180 seconds. Step 3: Combined distance covered = 20 × 180 = 3600 m. Step 4: Number of meetings = Total distance ÷ Track circumference = 3600 ÷ 600 = 6 times.

Question 8

A and B run on a circular track of 800 m. A runs at 10 m/s and B runs at 6 m/s in the same direction. They start together. After how much time will A be exactly 200 m ahead of B on the track (measured along the track)?

Accepted Answer

Step 1: For A to be 200 m ahead of B on the track, A must gain 200 m on B. Step 2: Relative speed = 10 - 6 = 4 m/s. Step 3: Time = Distance ÷ Relative Speed = 200 ÷ 4 = 50 seconds.

Question 9

P and Q start from opposite ends of a circular track of circumference 500 m. P runs at 12 m/s and Q runs at 8 m/s towards each other. How many times will they meet in 50 seconds?

Accepted Answer

Step 1: When moving towards each other on a circular track, relative speed = 12 + 8 = 20 m/s. Step 2: In 50 seconds, combined distance covered = 20 × 50 = 1000 m. Step 3: Number of meetings = Total distance ÷ Track circumference = 1000 ÷ 500 = 2 times.

Question 10

Two cyclists start from the same point on a circular path of length 1200 m. Cyclist X travels at 15 m/s and Cyclist Y travels at 9 m/s, both in the same direction. After X completes 5 full laps, how many complete laps will Y have completed?

Accepted Answer

Step 1: Time for X to complete 5 laps = (5 × 1200) ÷ 15 = 6000 ÷ 15 = 400 seconds. Step 2: In 400 seconds, distance covered by Y = 9 × 400 = 3600 m. Step 3: Number of complete laps by Y = 3600 ÷ 1200 = 3 laps.

Question 11

Two athletes, X and Y, run on a circular track of 600 m. X runs at 12 m/s and Y runs at 8 m/s, both starting from the same point in the same direction. After X completes 15 laps, X stops. Y continues and reaches the point where X stopped after running for an additional 75 seconds. What is the total distance covered by Y from the start?

Accepted Answer

Step 1: Time for X to complete 15 laps = (15 × 600) ÷ 12 = 9000 ÷ 12 = 750 seconds. Step 2: Position of X after 15 laps = starting point (0 metres on the track). Step 3: Distance covered by Y in 750 seconds = 8 × 750 = 6000 metres. Step 4: Laps by Y in 750 seconds = 6000 ÷ 600 = 10 laps. Step 5: Position of Y after 750 seconds = starting point (0 metres on the track). Step 6: Y continues for 75 more seconds to reach X's stopping point (which is the starting point). Step 7: Distance by Y in additional 75 seconds = 8 × 75 = 600 metres = 1 lap. Step 8: Total distance by Y = 6000 + 600 = 6600 metres.

Question 12

Two cyclists start from opposite ends of a circular track of circumference 600 m. Cyclist X travels at 12 m/s and Cyclist Y travels at 18 m/s, both moving towards each other. How many times will they meet in the first 5 minutes?

Accepted Answer

Step 1: When moving towards each other on a circular track, relative speed = 12 + 18 = 30 m/s. Step 2: They meet when the sum of distances covered equals the track circumference. Step 3: Time for first meeting = 600 ÷ 30 = 20 seconds. Step 4: After the first meeting, they meet again every 20 seconds. Step 5: Total time = 5 minutes = 300 seconds. Step 6: Number of meetings = 300 ÷ 20 = 15 times.

SBI Clerk Circular Track & Meeting

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60-Second Revision — Circular Track & Meeting