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 (i.e., be exactly one full lap ahead)?

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. Therefore, answer is C.

Question 2

On a circular track of 1200 m, two runners X and Y start from the same point. X runs at 15 m/s and Y runs at 9 m/s in the same direction. At what time will X first meet Y again after they start (i.e., X catches up to Y)?

Accepted Answer

Step 1: Relative speed of X with respect to Y = 15 - 9 = 6 m/s. Step 2: For X to catch up to Y (meet again), X must cover one full lap more than Y, meaning X must gain 1200 m on Y. Step 3: Time = Distance ÷ Relative Speed = 1200 ÷ 6 = 200 seconds.

Question 3

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 10 minutes?

Accepted Answer

Step 1: Since they move towards each other on a circular track, their relative speed = 12 + 18 = 30 m/s. Step 2: Time for first meeting = 600 ÷ 30 = 20 seconds. Step 3: After the first meeting, they continue and meet again every 20 seconds (the relative speed and track length remain constant). Step 4: Total time = 10 minutes = 600 seconds. Step 5: Number of meetings = 600 ÷ 20 = 30 times.

Question 4

Two runners, A and B, start simultaneously from the same point on a circular track of length 400 m. 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 means A must gain 400 m on B. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 3 = 133.33 seconds. However, checking: in 133.33 seconds, A covers 8 × 133.33 = 1066.67 m and B covers 5 × 133.33 = 666.67 m. Difference = 400 m (exactly one lap). Therefore, answer is 133⅓ seconds or approximately 133 seconds (if rounding to nearest integer for RRB format, the exact answer is 400/3 = 133.33 seconds).

Question 5

Two friends, P and Q, jog on a circular track of 800 m. P's speed is 6 m/s and Q's speed is 4 m/s. They start from the same point at the same time, running in the same direction. How many times will P lap Q in 20 minutes?

Accepted Answer

Step 1: Relative speed of P with respect to Q = 6 - 4 = 2 m/s. Step 2: Time for P to lap Q once (gain 800 m) = 800 ÷ 2 = 400 seconds. Step 3: Total time = 20 minutes = 1200 seconds. Step 4: Number of times P laps Q = 1200 ÷ 400 = 3 times.

Question 6

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 (or 20/3 m/s). Step 3: Relative speed = 10 - 6.67 = 3.33 m/s (or 10/3 m/s). Step 4: For A to be 2 laps ahead, A must gain 2 × 500 = 1000 m on B. Step 5: Time = 1000 ÷ 3.33 = 300 seconds (or 1000 ÷ (10/3) = 1000 × 3/10 = 300 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 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: Since both runners move in the same direction on a circular track, the relative speed is the difference of their speeds: 8 − 6 = 2 m/s. Step 2: For A to lap B, A must gain exactly one full lap (400 metres) on B. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds. Therefore, answer is C.

Question 8

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 (i.e., A will be exactly 400 metres ahead of B on the track)?

Accepted Answer

Step 1: Identify that A lapping B means A covers exactly 400 m more than B on the circular track. Step 2: For the second lapping, A must be 800 m ahead in absolute distance (two full laps relative to B). Step 3: Relative speed = 8 − 5 = 3 m/s. Step 4: Time = Distance ÷ Relative Speed = 800 ÷ 3 = 266.67 seconds. Step 5: Verify: In 266.67 seconds, A covers 8 × 266.67 = 2133.33 m, B covers 5 × 266.67 = 1333.33 m. Difference = 800 m = exactly 2 laps of 400 m. Therefore, answer is C.

RRB Group D 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