Question 1

Two runners A and B start from the same point on a circular track of 800 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: Time = 10 minutes = 600 seconds. Step 3: Distance covered by A relative to B = 4 × 600 = 2400 m. Step 4: Number of laps = 2400 ÷ 800 = 3 times.

Question 2

A man runs around a circular track of circumference 500 m at a constant speed. He completes one lap in 50 seconds. What is his speed in m/s?

Accepted Answer

Step 1: Speed is defined as distance covered per unit time. Step 2: Distance = 500 m, Time = 50 seconds. Step 3: Speed = Distance ÷ Time = 500 ÷ 50 = 10 m/s.

Question 3

Two joggers start from the same point on a circular track of 800 metres. Jogger X runs at 4 m/s and Jogger Y runs at 6 m/s in the same direction. After how many seconds will Y be exactly 200 metres ahead of X on the track (measured along the track)?

Accepted Answer

Step 1: Relative speed = 6 − 4 = 2 m/s. Step 2: For Y to be 200 metres ahead of X on the circular track, Y must cover 200 metres more than X relative to X's position. Step 3: Time = Distance ÷ Relative Speed = 200 ÷ 2 = 100 seconds.

Question 4

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: Time for A to lap B once = 500 ÷ 5 = 100 seconds. Step 4: Number of overtakes in 500 seconds = 500 ÷ 100 = 5 times.

Question 5

Two runners start from the same point on a circular track of length 400 m. 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: Relative speed = 8 - 6 = 2 m/s (since they run in the same direction). Step 2: For A to lap B, A must cover one complete extra lap = 400 m. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 6

Two cyclists start from opposite ends of a circular track of 600 m 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, relative speed = 10 + 14 = 24 m/s. Step 2: They meet when the sum of distances covered equals the track length = 600 m. Step 3: Time = 600 ÷ 24 = 25 seconds.

Question 7

Two persons P and Q start simultaneously from the same point on a circular track of 1200 m and run in opposite directions at speeds of 9 m/s and 15 m/s respectively. After how many seconds will they meet for the second time?

Accepted Answer

Step 1: Relative speed = 9 + 15 = 24 m/s (opposite directions). Step 2: For the first meeting, they cover the full track: Time₁ = 1200 ÷ 24 = 50 seconds. Step 3: For the second meeting, they again cover the full track from their first meeting point: Time₂ = 50 seconds. Step 4: Total time = 50 + 50 = 100 seconds.

Question 8

Two runners, A and B, start running simultaneously 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. 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 9

Two cyclists start from the same point on a circular track of circumference 600 metres and travel in opposite directions. Their speeds are 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 in opposite directions, relative speed = 12 + 18 = 30 m/s. Step 2: They meet when the sum of distances covered equals the track circumference = 600 metres. Step 3: Time = Distance ÷ Relative Speed = 600 ÷ 30 = 20 seconds.

Question 10

Two friends, P and Q, jog on a circular path of length 800 m. P jogs at 6 m/s and Q jogs at 4 m/s, both starting from the same point in the same direction. How many complete laps will P have jogged when they meet for the third time?

Accepted Answer

Step 1: Relative speed = 6 - 4 = 2 m/s. Step 2: For each meeting, P must gain 800 m on Q. Step 3: Time for each meeting = 800 ÷ 2 = 400 seconds. Step 4: For third meeting, total time = 3 × 400 = 1200 seconds. Step 5: Distance covered by P = 6 × 1200 = 7200 m. Step 6: Number of laps = 7200 ÷ 800 = 9 laps.

Question 11

On a circular track of 1200 m, two runners A and B start from the same point. A runs at 15 m/s and B runs at 9 m/s in the same direction. If they start at the same time, 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 complete lap (1200 m) on B. Step 2: Relative speed = 15 - 9 = 6 m/s. Step 3: Time for first lapping = 1200 ÷ 6 = 200 seconds. Step 4: For second lapping, A must gain 2 × 1200 = 2400 m on B. Step 5: Time = 2400 ÷ 6 = 400 seconds.

Question 12

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 18 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, they meet when combined distance = track length (for first meeting), then every track length thereafter. Step 2: Relative speed = 12 + 18 = 30 m/s. Step 3: Time for first meeting = 600 ÷ 30 = 20 seconds. Step 4: In 5 minutes (300 seconds), number of meetings = 300 ÷ 20 = 15 times.

Question 13

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

Accepted Answer

Step 1: When moving in opposite directions on a circular track, relative speed = 6 + 4 = 10 m/s. Step 2: Time for first meeting = 800 ÷ 10 = 80 seconds. Step 3: For the second meeting, they must cover the track length again relative to each other. Step 4: Time for second meeting = 2 × 80 = 160 seconds.

Question 14

Two runners A and B start from the same point on a circular track of length 400 metres and run in the SAME direction. A runs at 8 m/s and B runs at 5 m/s. After how many seconds will A first overtake B?

Accepted Answer

Step 1: When running in the same direction, the relative speed = 8 – 5 = 3 m/s. Step 2: A overtakes B when A has covered exactly one full lap MORE than B, i.e., the relative distance = 400 m. Step 3: Time = Relative Distance / Relative Speed = 400 / 3 = 133.33 seconds. Therefore, A first overtakes B after 400/3 ≈ 133.33 seconds, which is 133⅓ seconds.

Question 15

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 and run in the same direction, after how many seconds will A be exactly 200 m ahead of B on the track?

Accepted Answer

Step 1: Speed of A = 500 ÷ 50 = 10 m/s. Speed of B = 500 ÷ 75 = 6.67 m/s. Step 2: For A to be 200 m ahead, relative distance = 200 m. Step 3: Relative speed = 10 - 6.67 = 3.33 m/s. Step 4: Time = 200 ÷ 3.33 = 60 seconds. Verification: A covers 10 × 60 = 600 m (1 full lap + 100 m), B covers 6.67 × 60 = 400 m. Difference = 200 m. ✓

Question 16

Two athletes, P and Q, run on a circular track of 800 m. P runs at 16 m/s and Q runs at 12 m/s in the same direction, starting from the same point. At what time will they meet for the third time?

Accepted Answer

Step 1: Relative speed = 16 − 12 = 4 m/s. Step 2: Time for P to lap Q once (first meeting) = 800 ÷ 4 = 200 seconds. Step 3: For the third meeting, P must lap Q twice more (second and third meetings occur at 2 × 200 = 400 seconds and 3 × 200 = 600 seconds respectively). Step 4: Third meeting occurs at 600 seconds.

Question 17

Two cyclists start from opposite ends of a circular track of circumference 600 m at the same time. They travel 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 circumference (or a multiple thereof). Step 2: Relative 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 times.

Question 18

On a circular track of 500 metres, Runner P starts from point X and runs at 10 m/s. Runner Q starts from the same point X, 5 seconds later, and runs at 15 m/s in the same direction. After Q starts, how many seconds will it take for Q to lap P for the first time?

Accepted Answer

Step 1: When Q starts, P has already covered 10 × 5 = 50 metres. Step 2: Q needs to gain 500 metres (one full lap) on P. Step 3: Q's head start distance to overcome = 50 metres. Step 4: Relative speed = 15 − 10 = 5 m/s. Step 5: Time for Q to lap P = (500 + 50) ÷ 5 = 550 ÷ 5 = 110 seconds.

Question 19

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 in the same direction, starting from the same point simultaneously. How many times will M lap N in 10 minutes?

Accepted Answer

Step 1: Relative speed = 16 − 12 = 4 m/s. Step 2: Time = 10 minutes = 600 seconds. Step 3: Total relative distance covered = 4 × 600 = 2400 metres. Step 4: Number of laps = 2400 ÷ 800 = 3 laps.

Question 20

Two runners, X and Y, start from the same point on a circular track of 900 m. X runs at 18 m/s and Y runs at 9 m/s in the same direction. If they start at the same time, at what distance from the starting point will they meet for the second time?

Accepted Answer

Step 1: Relative speed = 18 − 9 = 9 m/s. Step 2: Time for first meeting (X laps Y once) = 900 ÷ 9 = 100 seconds. Step 3: Time for second meeting = 2 × 100 = 200 seconds. Step 4: At t = 200 seconds, Y's distance = 9 × 200 = 1800 m. Step 5: Y's position on track = 1800 mod 900 = 0 m (back at starting point). Step 6: X's distance = 18 × 200 = 3600 m. X's position = 3600 mod 900 = 0 m. Both are at the starting point, so they meet at 0 m (or 900 m, which is the same point).

SSC CHSL 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