Question 1

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)?

Accepted Answer

Step 1: When two objects move in the same direction on a circular track, the faster one laps the slower one when the difference in distances covered equals the track length. Step 2: Relative speed = 8 − 6 = 2 m/s. Step 3: Time to lap = Track length ÷ Relative speed = 400 ÷ 2 = 200 seconds.

Question 2

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)?

Accepted Answer

Step 1: When two objects move in the same direction on a circular track, the relative speed is the difference of their speeds. Relative speed = 8 − 6 = 2 m/s. Step 2: For A to lap B, A must gain a distance equal to the track length (400 m) on B. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds. Therefore, the answer is 200 seconds.

Question 3

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?

Accepted Answer

Step 1: For A to lap B, A must gain one full lap (400 m) on B. The relative speed is 8 − 5 = 3 m/s. Step 2: Time for first lap = 400 ÷ 3 = 133.33 seconds. Step 3: For the second lap, A must gain another 400 m on B at the same relative speed. Time for second lap = 400 ÷ 3 = 133.33 seconds. Step 4: Total time = 133.33 + 133.33 = 266.67 seconds = 800/3 seconds ≈ 266⅔ seconds. Alternatively, after time t, A covers 8t metres and B covers 5t metres. For A to lap B twice, A must be exactly 800 m ahead: 8t − 5t = 800, so 3t = 800, giving t = 800/3 = 266⅔ seconds.

Question 4

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?

Accepted Answer

Step 1: Find the time each runner takes to complete one full lap. A: 1200/4 = 300 s, B: 1200/6 = 200 s, C: 1200/10 = 120 s. Step 2: To find when all three meet at the starting point, take LCM of 300, 200, and 120. Step 3: 300 = 2² × 3 × 5², 200 = 2³ × 5², 120 = 2³ × 3 × 5. LCM = 2³ × 3 × 5² = 8 × 3 × 25 = 600. Therefore, all three meet at the starting point after 600 seconds.

Question 5

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?

Accepted Answer

Step 1: Relative speed = 9 - 6 = 3 m/s. Step 2: For X to lap Y, X must gain 1200 m on Y. Step 3: Time taken = 1200 ÷ 3 = 400 seconds. Step 4: Distance covered by Y in 400 seconds = 6 × 400 = 2400 m.

Question 6

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)?

Accepted Answer

Step 1: Relative speed = 8 - 6 = 2 m/s (since both run in the same direction). Step 2: For A to lap B, A must cover one full lap more than B, which is 400 metres relative distance. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 7

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?

Accepted Answer

Step 1: When running in opposite directions, relative speed = 12 + 8 = 20 m/s. Step 2: For the first meeting, they cover a combined distance equal to the circumference = 800 metres. Time for first meeting = 800 ÷ 20 = 40 seconds. Step 3: For the second meeting, they must cover a combined distance of 2 × circumference = 1600 metres. Step 4: Time for second meeting = 1600 ÷ 20 = 80 seconds.

Question 8

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)?

Accepted Answer

Step 1: Relative speed = 6 - 4 = 2 m/s. Step 2: For them to meet at the same point again, A must lap B, meaning A gains one full lap = 360 metres. Step 3: Time for first meeting (after start) = 360 ÷ 2 = 180 seconds. Step 4: For the second meeting, A must gain another full lap = 360 metres. Step 5: Time for second meeting = 2 × 180 = 360 seconds.

Question 9

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?

Accepted Answer

Step 1: Time taken by first athlete to complete 10 laps = (10 × 300) ÷ 6 = 3000 ÷ 6 = 500 seconds. Step 2: Distance covered by second athlete in 500 seconds = 4 × 500 = 2000 metres. Step 3: Number of complete laps by second athlete = 2000 ÷ 300 = 6.67, so 6 complete laps.

Question 10

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?

Accepted Answer

Step 1: Distance covered by A in 5 laps = 5 × 500 = 2500 m. Step 2: Time taken by A = 2500 ÷ 10 = 250 seconds. Step 3: In 250 seconds, distance covered by B = 7 × 250 = 1750 m. Step 4: Number of complete laps by B = 1750 ÷ 500 = 3.5 laps, so 3 complete laps.

Question 11

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?

Accepted Answer

Step 1: Relative speed = 12 - 8 = 4 m/s. Step 2: In 10 minutes = 600 seconds, the relative distance covered = 4 × 600 = 2400 m. Step 3: Number of laps = 2400 ÷ 600 = 4 times.

Question 12

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?

Accepted Answer

Step 1: Since they cycle in opposite directions, relative speed = 12 + 8 = 20 m/s. Step 2: They will meet when the sum of distances covered equals the track length (600 metres). Step 3: Time = Distance ÷ Relative Speed = 600 ÷ 20 = 30 seconds.

Question 13

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)?

Accepted Answer

Step 1: Relative speed of A with respect to B = 8 − 6 = 2 m/s. Step 2: For A to lap B, A must cover one full lap more than B, which is 400 metres relative distance. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 14

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?

Accepted Answer

Step 1: When running in opposite directions, they meet when combined distance equals the track length. Step 2: Combined speed = 6 + 4 = 10 m/s. Step 3: Time for first meeting = 800 ÷ 10 = 80 seconds. Step 4: For second meeting, they must cover the track length again from their first meeting point. Step 5: Time for second meeting = 2 × 80 = 160 seconds.

Question 15

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?

Accepted Answer

Step 1: When moving towards each other on a circular track, they meet when the sum of distances covered equals the track length. Step 2: Combined speed = 12 + 18 = 30 m/s. Step 3: Time to first meeting = Track length ÷ Combined speed = 600 ÷ 30 = 20 seconds.

Question 16

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)?

Accepted Answer

Step 1: When A laps B, A covers exactly 400 metres more than B. Step 2: Relative speed = 8 − 6 = 2 m/s. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 17

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?

Accepted Answer

Step 1: Since they cycle towards each other on a circular track, their relative speed = 10 + 5 = 15 m/s. Step 2: They will meet when the sum of distances covered equals the circumference = 600 metres. Step 3: Time = Distance ÷ Relative Speed = 600 ÷ 15 = 40 seconds.

Question 18

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?

Accepted Answer

Step 1: Relative speed = 15 - 9 = 6 m/s. Step 2: For M to lap N, M must gain 1200 metres (one full lap) on N. Step 3: Time taken = 1200 ÷ 6 = 200 seconds. Step 4: Distance covered by N in 200 seconds = 9 × 200 = 1800 metres.

Question 19

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?

Accepted Answer

Step 1: Relative speed of X with respect to Y = 6 − 4 = 2 m/s. Step 2: For X to be 150 metres ahead of Y on the track, X must gain 150 metres relative to Y. Step 3: Time = Distance ÷ Relative Speed = 150 ÷ 2 = 75 seconds.

Question 20

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?

Accepted Answer

Step 1: When two objects move towards each other on a circular track, they meet when the sum of distances covered equals the track length. Step 2: Combined speed = 10 + 15 = 25 m/s. Step 3: Time to first meeting = Track length ÷ Combined speed = 500 ÷ 25 = 20 seconds.

Question 21

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?

Accepted Answer

Step 1: Speed of A = 500 ÷ 50 = 10 m/s. Speed of B = 500 ÷ 100 = 5 m/s. Step 2: Relative speed = 10 - 5 = 5 m/s. Step 3: In 500 seconds, relative distance covered = 5 × 500 = 2500 metres. Step 4: Number of laps = 2500 ÷ 500 = 5 times.

Question 22

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?

Accepted Answer

Step 1: Speed of A = 500 ÷ 50 = 10 m/s. Speed of B = 500 ÷ 100 = 5 m/s. Step 2: Relative speed = 10 − 5 = 5 m/s. Step 3: For each overtake, A must gain one full lap (500 m) on B. Time for one overtake = 500 ÷ 5 = 100 seconds. Step 4: Number of overtakes in 500 seconds = 500 ÷ 100 = 5 times.

Question 23

Two runners start from the same point on a circular track of circumference 900 m. Runner X runs at 15 m/s and Runner Y runs at 9 m/s in the same direction. What is the difference in distances covered by them when X laps Y for the second time?

Accepted Answer

Step 1: Relative speed = 15 - 9 = 6 m/s. Step 2: For X to lap Y twice, X must gain 2 × 900 = 1800 m on Y. Step 3: Time taken = 1800 / 6 = 300 seconds. Step 4: Distance covered by X = 15 × 300 = 4500 m. Step 5: Distance covered by Y = 9 × 300 = 2700 m. Step 6: Difference = 4500 - 2700 = 1800 m.

Question 24

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

Accepted Answer

Step 1: When moving towards each other on a circular track, relative speed = 12 + 8 = 20 m/s. Step 2: Time for one meeting = Track length / Relative speed = 600 / 20 = 30 seconds. Step 3: In 5 minutes (300 seconds), number of meetings = 300 / 30 = 10 times.

CTET Paper II Circular Track & Meeting

CTET Paper II Circular Track & Meeting — Past Exam Questions

Circular Track & Meeting— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Circular Track & Meeting — Practice Questions

60-Second Revision — Circular Track & Meeting