Question 1

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 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 lap more than B, which is 400 metres. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 2

Two athletes P and Q run on a circular track of 400 metres. P runs at 12 m/s and Q runs at 8 m/s, both starting from the same point in the same direction. What is the time interval between their first and second meetings?

Accepted Answer

Step 1: Relative speed = 12 - 8 = 4 m/s (same direction). Step 2: For each meeting, P must lap Q, which means P covers 400 metres more than Q. Step 3: Time for one lapping = 400 ÷ 4 = 100 seconds. Step 4: First meeting occurs at 100 seconds, second meeting at 200 seconds. Step 5: Time interval = 200 - 100 = 100 seconds.

Question 3

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

Accepted Answer

Step 1: Since they cycle towards each other (opposite directions), relative speed = 10 + 15 = 25 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 ÷ 25 = 24 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 times A overtakes B in 500 seconds = 500 ÷ 100 = 5 times.

Question 5

Two joggers start from the same point on a circular track of 800 metres and jog in opposite directions at 6 m/s and 4 m/s respectively. How many seconds after the start will they meet for the second time?

Accepted Answer

Step 1: Since they jog in opposite directions, relative speed = 6 + 4 = 10 m/s. Step 2: For the first meeting, they cover the entire track length together = 800 metres. Time for first meeting = 800 ÷ 10 = 80 seconds. Step 3: For the second meeting, they again need to cover 800 metres at relative speed 10 m/s. Step 4: Total time for second meeting = 80 + 80 = 160 seconds.

Question 6

On a circular track of 1200 metres, runner X takes 120 seconds to complete one lap while runner Y takes 150 seconds. Starting together from the same point in the same direction, after how many seconds will X be exactly 2 laps ahead of Y?

Accepted Answer

Step 1: Speed of X = 1200 ÷ 120 = 10 m/s. Speed of Y = 1200 ÷ 150 = 8 m/s. Step 2: Relative speed = 10 - 8 = 2 m/s. Step 3: For X to be 2 laps ahead, X must cover 2 × 1200 = 2400 metres more than Y. Step 4: Time = 2400 ÷ 2 = 1200 seconds.

Question 7

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 first time?

Accepted Answer

Step 1: Relative speed of A with respect to B = 8 − 5 = 3 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 ÷ 3 = 133.33 seconds. However, checking: at 133.33 s, A covers 8 × 133.33 = 1066.67 m, B covers 5 × 133.33 = 666.67 m. Difference = 400 m (one lap). Therefore, answer is 133⅓ seconds or 400/3 seconds.

Question 8

Two cyclists start from opposite ends of a circular track of circumference 600 metres 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 the first 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: In 5 minutes (300 seconds), number of meetings = 300 ÷ 30 = 10 times.

Question 9

Two joggers start from the same point on a circular track of length 800 metres. Jogger X runs at 6 m/s and Jogger Y runs at 4 m/s in the same direction. How many times will X lap Y in 20 minutes?

Accepted Answer

Step 1: Relative speed = 6 − 4 = 2 m/s. Step 2: Time for one lap (X lapping Y) = 800 ÷ 2 = 400 seconds. Step 3: Total time = 20 minutes = 1200 seconds. Step 4: Number of laps = 1200 ÷ 400 = 3 times.

Question 10

On a circular track of 1200 metres, two runners P and Q start from the same point. P runs at 15 m/s and Q runs at 9 m/s in the same direction. At what time will P and Q meet for the second time?

Accepted Answer

Step 1: Relative speed = 15 − 9 = 6 m/s. Step 2: For the first meeting (first lap by P over Q), time = 1200 ÷ 6 = 200 seconds. Step 3: For the second meeting, P must lap Q twice, so distance to cover = 2 × 1200 = 2400 metres. Step 4: Time = 2400 ÷ 6 = 400 seconds.

Question 11

Two athletes start from opposite ends of a circular track of circumference 1000 metres and run towards each other. Athlete M runs at 10 m/s and Athlete N runs at 15 m/s. If they start at the same time, in how many seconds will they meet for the third time?

Accepted Answer

Step 1: Combined speed (towards each other) = 10 + 15 = 25 m/s. Step 2: For the first meeting, they together cover the full track: time = 1000 ÷ 25 = 40 seconds. Step 3: For the third meeting, they together cover 3 full tracks: distance = 3 × 1000 = 3000 metres. Step 4: Time = 3000 ÷ 25 = 120 seconds.

Question 12

Two cyclists start from opposite ends of a circular track of circumference 600 metres at the same time. Cyclist X travels at 12 m/s and Cyclist Y travels at 8 m/s. They meet for the second time after how many seconds?

Accepted Answer

Step 1: Since they start from opposite ends and move towards each other, their relative speed = 12 + 8 = 20 m/s. Step 2: For the first meeting, they together cover the full track length = 600 m. Time to first meeting = 600 ÷ 20 = 30 seconds. Step 3: For the second meeting, they must together cover two full track lengths = 1200 m (after the first meeting, they continue and meet again after covering another full lap relative to the starting configuration). Step 4: Time to second meeting = 1200 ÷ 20 = 60 seconds.

Question 13

On a circular track of 500 metres, Runner P starts from point A and runs at 10 m/s, while Runner Q starts from point A at the same time and runs at 6 m/s in the same direction. After P completes exactly 5 full laps, how many complete laps will Q have completed?

Accepted Answer

Step 1: Time taken by P to complete 5 laps = (5 × 500) ÷ 10 = 2500 ÷ 10 = 250 seconds. Step 2: In 250 seconds, distance covered by Q = 6 × 250 = 1500 metres. Step 3: Number of complete laps by Q = 1500 ÷ 500 = 3 complete laps.

Question 14

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, both starting from the same point in the same direction. How many times will M lap N in 20 minutes?

Accepted Answer

Step 1: Convert 20 minutes to seconds = 20 × 60 = 1200 seconds. Step 2: Relative speed of M with respect to N = 16 − 12 = 4 m/s. Step 3: In 1200 seconds, relative distance covered by M = 4 × 1200 = 4800 metres. Step 4: Number of times M laps N = 4800 ÷ 800 = 6 times.

Question 15

On a circular track, Racer A and Racer B start from the same point. A runs at 15 m/s and B runs at 9 m/s in the same direction. The track length is such that A completes one lap in 60 seconds. After how many seconds will A and B meet again at the starting point simultaneously?

Accepted Answer

Step 1: Track length = Speed of A × Time for one lap = 15 × 60 = 900 metres. Step 2: Time for B to complete one lap = 900 ÷ 9 = 100 seconds. Step 3: For both to meet at the starting point simultaneously, the time must be a common multiple of their individual lap times. LCM(60, 100) = 300 seconds. Step 4: Verify: In 300 seconds, A completes 300 ÷ 60 = 5 laps; B completes 300 ÷ 100 = 3 laps. Both are at the starting point.

Question 16

Two joggers, X and Y, start from opposite ends of a circular track of 1200 metres. X jogs at 8 m/s and Y jogs at 10 m/s towards each other. After their first meeting, they continue jogging. At what distance from X's starting point will they meet for the third time?

Accepted Answer

Step 1: Combined speed = 8 + 10 = 18 m/s. Step 2: For the first meeting, combined distance = 1200 m. Time to first meeting = 1200 ÷ 18 = 66.67 seconds. Distance covered by X = 8 × 66.67 = 533.33 m from X's start. Step 3: For the third meeting, combined distance = 3 × 1200 = 3600 m. Time to third meeting = 3600 ÷ 18 = 200 seconds. Step 4: Distance covered by X in 200 seconds = 8 × 200 = 1600 m. Step 5: Since track is 1200 m, X's position = 1600 mod 1200 = 400 m from starting point.

SBI PO Circular Track & Meeting

SBI PO Circular Track & Meeting — Past Exam Questions

Circular Track & Meeting— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Circular Track & Meeting