Question 1

Two runners start from the same point on a circular track of 300 metres. Runner P runs at 12 m/s and Runner Q runs at 8 m/s in opposite directions. After how many seconds will they meet for the third time?

Accepted Answer

Step 1: Running in opposite directions, combined speed = 12 + 8 = 20 m/s. Step 2: For first meeting, they cover 300 m together: time = 300 ÷ 20 = 15 seconds. Step 3: For each subsequent meeting, they cover another 300 m together. Step 4: For third meeting: time = 3 × 15 = 45 seconds.

Question 2

A jogger runs on a circular track of 250 metres at a constant speed of 10 m/s. How many complete laps will the jogger finish in 5 minutes?

Accepted Answer

Step 1: Convert 5 minutes to seconds: 5 × 60 = 300 seconds. Step 2: Distance covered = speed × time = 10 × 300 = 3000 metres. Step 3: Number of complete laps = 3000 ÷ 250 = 12 laps.

Question 3

Two runners start from the same point on a circular track of length 400 metres. Runner A runs at 8 m/s and Runner B runs at 6 m/s in the same direction. After how many seconds will Runner A lap Runner B for the first time?

Accepted Answer

Step 1: For A to lap B, A must gain one full 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 4

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 14 m/s respectively. In how many seconds will they meet for the first time?

Accepted Answer

Step 1: Since they move towards each other on a circular track, they approach each other. Step 2: Combined speed = 10 + 14 = 24 m/s. Step 3: They meet when combined distance covered = track length = 600 m. Step 4: Time = 600 ÷ 24 = 25 seconds.

Question 5

A runner completes one lap of a circular track in 40 seconds. Another runner completes one lap in 50 seconds. Both start together from the same point in the same direction. After how many seconds will the faster runner lap the slower runner for the second time?

Accepted Answer

Step 1: Faster runner gains one lap on slower runner every time their relative time equals the LCM concept. Step 2: In 1 second, faster runner covers 1/40 of track, slower covers 1/50. Step 3: Relative progress per second = 1/40 - 1/50 = (5-4)/200 = 1/200 of track. Step 4: To gain 2 full laps (2 × 1 = 2 units), time = 2 ÷ (1/200) = 400 seconds.

Question 6

Two athletes run on a circular track of 500 metres. Athlete X runs at 5 m/s and Athlete Y runs at 3 m/s in the same direction, starting from the same point. How many times will X lap Y in 10 minutes?

Accepted Answer

Step 1: Relative speed = 5 - 3 = 2 m/s. Step 2: Time = 10 minutes = 600 seconds. Step 3: Distance gained by X on Y = 2 × 600 = 1200 metres. Step 4: Number of laps = 1200 ÷ 500 = 2.4, so X laps Y exactly 2 times (the third lap is incomplete).

Question 7

Two friends start running from the same point on a circular track of 800 m. They run in opposite directions at speeds of 6 m/s and 4 m/s respectively. At what time will they meet for the third time?

Accepted Answer

Step 1: When running in opposite directions, relative speed = 6 + 4 = 10 m/s. Step 2: Time for first meeting = 800 ÷ 10 = 80 seconds. Step 3: Each subsequent meeting occurs at the same interval (80 seconds) because the relative speed remains constant. Step 4: Time for third meeting = 3 × 80 = 240 seconds.

Question 8

Two athletes start from the same point on a circular track of 400 m. Athlete P runs at 12 m/s and Athlete Q runs at 8 m/s in the same direction. How many times will P lap Q in 20 minutes?

Accepted Answer

Step 1: Relative speed = 12 - 8 = 4 m/s. Step 2: Time for one lapping = 400 ÷ 4 = 100 seconds. Step 3: Total time = 20 minutes = 1200 seconds. Step 4: Number of lappings = 1200 ÷ 100 = 12 times.

Question 9

Two cyclists start from opposite ends of a circular track of 600 m 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 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 first meeting = 600 ÷ 20 = 30 seconds. Step 3: After first meeting, they meet again every time their combined distance equals the track length. Step 4: In 5 minutes (300 seconds), number of meetings = 300 ÷ 30 = 10 times.

Question 10

A and B run on a circular track of 500 m. A completes one lap in 50 seconds, while B completes one lap in 75 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: Speed of A = 500 ÷ 50 = 10 m/s. Step 2: Speed of B = 500 ÷ 75 = 6.67 m/s. Step 3: For A to be 2 laps ahead, A must gain 2 × 500 = 1000 m on B. Step 4: Relative speed = 10 - 6.67 = 3.33 m/s. Step 5: Time = 1000 ÷ 3.33 = 300 seconds. Verification: A covers 10 × 300 = 3000 m = 6 laps; B covers 6.67 × 300 = 2000 m = 4 laps. Difference = 2 laps. ✓

Question 11

On a circular track of 1200 m, runner X takes 120 seconds to complete one lap, and runner Y takes 150 seconds. Both start together from the same point in the same direction. After how many seconds will X lap Y for the second time?

Accepted Answer

Step 1: Speed of X = 1200 ÷ 120 = 10 m/s. Step 2: Speed of Y = 1200 ÷ 150 = 8 m/s. Step 3: Relative speed = 10 - 8 = 2 m/s. Step 4: For one lapping (X gains 1200 m on Y), time = 1200 ÷ 2 = 600 seconds. Step 5: For second lapping, X must gain 2 × 1200 = 2400 m on Y. Step 6: Time = 2400 ÷ 2 = 1200 seconds.

Question 12

Two athletes start from point A on a circular track of 400 m. Athlete M runs at 20 m/s and Athlete N runs at 12 m/s, both in the same direction. M overtakes N for the second time at point B. What is the distance from A to B measured along the track?

Accepted Answer

Step 1: M overtakes N when M has covered exactly one more lap than N (first overtake), then two more laps (second overtake). Step 2: For the second overtake, M must gain 2 × 400 = 800 m on N. Step 3: Relative speed = 20 - 12 = 8 m/s. Step 4: Time for second overtake = 800 / 8 = 100 seconds. Step 5: Distance covered by N in 100 seconds = 12 × 100 = 1200 m. Step 6: Position of N on track = 1200 mod 400 = 200 m from point A.

Question 13

Two cyclists start from opposite ends of a circular track of circumference 600 m at the same time. They cycle towards each other at speeds of 12 m/s and 18 m/s respectively. How many times will they meet in the first 5 minutes?

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 (or multiples thereof). Step 2: Combined speed = 12 + 18 = 30 m/s. Step 3: Time to first meeting = 600 / 30 = 20 seconds. Step 4: In 5 minutes (300 seconds), number of meetings = 300 / 20 = 15 meetings.

Question 14

Two runners start from the same point on a circular track of 800 m. Runner X runs at 16 m/s and Runner Y runs at 12 m/s in the same direction. After 2 minutes, what is the distance between them measured along the shorter arc of the track?

Accepted Answer

Step 1: Time = 2 minutes = 120 seconds. Step 2: Distance covered by X = 16 × 120 = 1920 m. Step 3: Distance covered by Y = 12 × 120 = 1440 m. Step 4: Difference in distance = 1920 - 1440 = 480 m. Step 5: Since the track is 800 m, X is 480 m ahead of Y on the track. The shorter arc distance = 480 m (since 480 < 400 is false; 480 < 800/2 is false, so we take 800 - 480 = 320 m as the shorter arc).

Question 15

A and B run on a circular track of 500 m. A runs at 10 m/s and B runs at 6 m/s, both in the same direction starting from the same point. After A completes 8 full laps, how many complete laps will B have completed?

Accepted Answer

Step 1: Time for A to complete 8 laps = (8 × 500) / 10 = 4000 / 10 = 400 seconds. Step 2: Distance covered by B in 400 seconds = 6 × 400 = 2400 m. Step 3: Number of complete laps by B = 2400 / 500 = 4.8 laps. Since we need complete laps, B completes 4 full laps.

SSC MTS Circular Track & Meeting

Circular Track & Meeting— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Circular Track & Meeting — Practice Questions

60-Second Revision — Circular Track & Meeting