Question 1

A man runs around a circular track of radius 35 m at a constant speed of 10 m/s. How long will it take him to complete exactly 3 full laps? (Use π = 22/7)

Accepted Answer

Step 1: Circumference of circular track = 2πr = 2 × (22/7) × 35 = 220 m. Step 2: Distance for 3 laps = 3 × 220 = 660 m. Step 3: Time = Distance ÷ Speed = 660 ÷ 10 = 66 seconds.

Question 2

A jogger runs on a circular track of circumference 400 m. He completes one lap in 50 seconds. What is his speed in m/s?

Accepted Answer

Step 1: Distance covered = circumference = 400 m. Step 2: Time taken = 50 seconds. Step 3: Speed = Distance ÷ Time = 400 ÷ 50 = 8 m/s.

Question 3

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 (same direction). Step 2: For A to lap B, A must cover one full lap more than B, which means A must gain 400 m on B. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 4

Two cyclists start from opposite ends of a circular track of circumference 600 m. They 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?

Accepted Answer

Step 1: When moving towards each other on a circular track, relative speed = 10 + 15 = 25 m/s. Step 2: They meet when the sum of distances covered equals the track circumference. Step 3: Time = 600 ÷ 25 = 24 seconds.

Question 5

Athlete A and Athlete B run on a circular track of 1200 metres. A runs at 15 m/s and B runs at 9 m/s, both starting from the same point in the same direction. At what distance from the starting point will A lap B for the first time?

Accepted Answer

Step 1: Relative speed = 15 - 9 = 6 m/s. Step 2: Time for A to lap B = 1200 ÷ 6 = 200 seconds. Step 3: Distance covered by A in 200 seconds = 15 × 200 = 3000 metres. Step 4: Position on track = 3000 mod 1200 = 3000 - 2(1200) = 3000 - 2400 = 600 metres from the starting point.

Question 6

On a circular track of 360 metres, two runners start together from the same point. Runner P completes the track in 40 seconds, while Runner Q completes it in 60 seconds. They run in the same direction. After how many seconds will P and Q meet again at the starting point?

Accepted Answer

Step 1: Speed of P = 360 ÷ 40 = 9 m/s. Step 2: Speed of Q = 360 ÷ 60 = 6 m/s. Step 3: Time for P to complete one lap = 40 seconds. Step 4: Time for Q to complete one lap = 60 seconds. Step 5: They meet at the starting point when the time elapsed is a common multiple of their lap times. Step 6: LCM(40, 60) = 120 seconds.

Question 7

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 5 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 full lap (400 m) on B. Step 2: Relative speed = 8 - 5 = 3 m/s. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 3 = 133.33 seconds. Step 4: Rounding to nearest practical value gives approximately 133⅓ seconds or 400/3 seconds.

Question 8

Two joggers, M and N, start from the same point on a circular track of 800 metres and jog in opposite directions. M jogs at 6 m/s and N jogs at 4 m/s. They meet every 80 seconds. How many times will they meet in 8 minutes?

Accepted Answer

Step 1: Combined speed = 6 + 4 = 10 m/s (opposite directions). Step 2: Distance covered together in one meeting cycle = 800 m. Step 3: Time between meetings = 800 ÷ 10 = 80 seconds (given, confirms calculation). Step 4: Total time = 8 minutes = 480 seconds. Step 5: Number of meetings = 480 ÷ 80 = 6 times.

Question 9

Two cyclists start from opposite ends of a circular track of 600 metres simultaneously and cycle towards each other. Cyclist P cycles at 12 m/s and Cyclist Q cycles at 8 m/s. How many seconds will it take for them to meet for the second time?

Accepted Answer

Step 1: For the first meeting, they together cover the full track length (600 m). Step 2: Combined speed = 12 + 8 = 20 m/s. Step 3: Time to first meeting = 600 ÷ 20 = 30 seconds. Step 4: For the second meeting, they must together cover 2 × 600 = 1200 m. Step 5: Time to second meeting = 1200 ÷ 20 = 60 seconds.

Question 10

On a circular track of 500 metres, Runner X and Runner Y start together from the same point and run in the same direction. X completes one lap in 50 seconds, while Y completes one lap in 62.5 seconds. After how many seconds will X be exactly 100 metres ahead of Y on the track (measured along the track)?

Accepted Answer

Step 1: Speed of X = 500 ÷ 50 = 10 m/s. Step 2: Speed of Y = 500 ÷ 62.5 = 8 m/s. Step 3: Relative speed = 10 - 8 = 2 m/s. Step 4: For X to be 100 m ahead, the relative distance gained = 100 m. Step 5: Time = 100 ÷ 2 = 50 seconds.

Question 11

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

Question 12

Two joggers start from the same point on a circular track of 800 m and run in opposite directions. Their speeds are in the ratio 3:2. They meet every 160 seconds. What is the speed of the faster jogger?

Accepted Answer

Step 1: Let speeds be 3k and 2k m/s. Step 2: When running in opposite directions, relative speed = 3k + 2k = 5k m/s. Step 3: They meet when combined distance = track length = 800 m. Step 4: Time between meetings = 800 ÷ (5k) = 160 seconds. Step 5: 800 ÷ (5k) = 160 → 5k = 800 ÷ 160 = 5 → k = 1. Step 6: Speed of faster jogger = 3k = 3 × 1 = 3 m/s.

Question 13

A runner completes a circular track of 1200 m in 4 minutes. Another runner starts from the same point 30 seconds later and runs at 6 m/s in the same direction. After how many seconds from the start of the first runner will they meet for the first time?

Accepted Answer

Step 1: Speed of first runner = 1200 ÷ 240 = 5 m/s. Step 2: Speed of second runner = 6 m/s. Step 3: Second runner starts 30 seconds late, so first runner covers 5 × 30 = 150 m in those 30 seconds. Step 4: When second runner starts, first runner is 150 m ahead. Step 5: Relative speed = 6 − 5 = 1 m/s. Step 6: For second runner to catch up 150 m: Time = 150 ÷ 1 = 150 seconds (from when second runner starts). Step 7: Total time from start of first runner = 30 + 150 = 180 seconds.

Question 14

Two athletes run on a circular track of 400 m. Athlete X runs at 10 m/s and Athlete Y runs at 6 m/s, both starting from the same point in the same direction. At what distance from the starting point will they meet for the second time?

Accepted Answer

Step 1: Relative speed = 10 − 6 = 4 m/s. Step 2: For first meeting, X must lap Y once: Time₁ = 400 ÷ 4 = 100 seconds. Step 3: For second meeting, X must lap Y twice: Time₂ = (2 × 400) ÷ 4 = 200 seconds. Step 4: Distance covered by Y in 200 seconds = 6 × 200 = 1200 m. Step 5: Position on track = 1200 mod 400 = 1200 − 3(400) = 1200 − 1200 = 0 m (starting point). Alternatively: Distance covered by X = 10 × 200 = 2000 m = 5 laps = back at starting point. Both meet at the starting point.

SSC CPO 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