Question 1

Two runners, A and B, start running 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 much time will A meet B again for the first time after the start?

Accepted Answer

Step 1: Since both runners move in the same direction on a circular track, A will meet B again when A completes exactly one full lap more than B.

Step 2: Relative speed = Speed of A - Speed of B = 8 - 5 = 3 m/s

Step 3: For A to lap B (gain one complete lap), the relative distance to be covered = Length of track = 400 m

Step 4: Time = Relative Distance / Relative Speed = 400 / 3 = 133.33 seconds

Step 5: Convert to mixed number: 133.33 = 133⅓ seconds = 400/3 seconds ≈ 133 seconds (approximately)

Alternatively: Time = 400/3 = 133⅓ seconds ≈ 2 minutes 13⅓ seconds

Therefore, A will meet B again after 400/3 seconds or approximately 133⅓ seconds.

Question 2

P and Q start running from the same point on a circular track of 1200 m in opposite directions. P runs at 8 m/s and Q runs at 7 m/s. How many seconds will it take for them to meet for the second time?

Accepted Answer

Step 1: Since they run in opposite directions, relative speed = 8 + 7 = 15 m/s. Step 2: For the first meeting, they cover the full track: Time = 1200 ÷ 15 = 80 seconds. Step 3: For the second meeting, they again cover the full track together: Time = 1200 ÷ 15 = 80 seconds. Step 4: Total time for second meeting = 80 + 80 = 160 seconds.

Question 3

Two cyclists start from the same point on a circular track of 1200 metres and run in opposite directions at speeds of 15 m/s and 9 m/s respectively. How many seconds after the start will they meet for the third time?

Accepted Answer

Step 1: When moving in opposite directions, relative speed = 15 + 9 = 24 m/s. Step 2: For each meeting, they together cover 1200 metres. Step 3: Time for each meeting = 1200 ÷ 24 = 50 seconds. Step 4: For the third meeting, total time = 3 × 50 = 150 seconds.

Question 4

Two athletes run on a circular track of 500 metres. Athlete X completes the track in 50 seconds, while Athlete Y completes it in 60 seconds. Starting together from the same point in the same direction, after how many seconds will X be exactly 1 lap ahead of Y?

Accepted Answer

Step 1: Speed of X = 500 ÷ 50 = 10 m/s. Speed of Y = 500 ÷ 60 = 8.33 m/s. Step 2: Relative speed = 10 - 8.33 = 1.67 m/s (or 5/3 m/s). Step 3: To be 1 lap ahead, X must gain 500 metres on Y. Step 4: Time = 500 ÷ (5/3) = 500 × (3/5) = 300 seconds.

Question 5

Two cyclists start from opposite ends of a circular track of circumference 600 m and cycle towards each other at speeds of 12 m/s and 18 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, their relative speed = 12 + 18 = 30 m/s. Step 2: They meet when the sum of distances covered equals the track circumference. Step 3: Time = 600 ÷ 30 = 20 seconds.

Question 6

Two cyclists start from the same point on a circular track of 600 metres and run in opposite directions. Their speeds are 12 m/s and 8 m/s respectively. In how many seconds will they meet for the second time?

Accepted Answer

Step 1: When moving in opposite directions, relative speed = 12 + 8 = 20 m/s. Step 2: For the first meeting, they together cover 600 metres: Time = 600 ÷ 20 = 30 seconds. Step 3: For the second meeting, they together cover another 600 metres: Time = 600 ÷ 20 = 30 seconds. Step 4: Total time for second meeting = 30 + 30 = 60 seconds.

Question 7

Two athletes start from the same point on a circular track of length 300 m. Athlete X runs at 6 m/s and Athlete Y runs at 4 m/s in the same direction. How much distance (in metres) will Y have covered when X laps Y for the second time?

Accepted Answer

Step 1: Relative speed = 6 − 4 = 2 m/s. Step 2: For X to lap Y once, X must gain 300 m on Y. Time for first lap = 300 ÷ 2 = 150 seconds. Step 3: For X to lap Y twice, X must gain 600 m on Y. Time for second lap = 600 ÷ 2 = 300 seconds. Step 4: Distance covered by Y in 300 seconds = 4 × 300 = 1200 m.

Question 8

A and B run on a circular track of 500 m. A completes one lap in 50 seconds, while B completes one lap in 100 seconds. If they start together from the same point and run in the same direction, how many times will A lap B before A completes 4 laps?

Accepted Answer

Step 1: A's speed = 500 ÷ 50 = 10 m/s. B's speed = 500 ÷ 100 = 5 m/s. Step 2: Relative speed = 10 − 5 = 5 m/s. Step 3: Time for A to complete 4 laps = (4 × 500) ÷ 10 = 200 seconds. Step 4: In 200 seconds, A gains on B: 5 × 200 = 1000 m = 2 full laps. Step 5: Therefore, A laps B exactly 2 times.

Question 9

A and B run on a circular track of 500 m. A completes one lap in 50 seconds, while B completes one lap in 100 seconds. If they start together from the same point and run in the same direction, how many times will A lap 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: In 500 seconds, A gains = 5 × 500 = 2500 m on B. Step 4: Number of laps = 2500 ÷ 500 = 5 times.

Question 10

Two joggers start from the same point on a circular path of 800 m and jog in the same direction. The faster jogger completes the path in 80 seconds, while the slower one takes 160 seconds. After how many seconds will the faster jogger be exactly 200 m ahead of the slower jogger?

Accepted Answer

Step 1: Speed of faster jogger = 800 ÷ 80 = 10 m/s. Speed of slower jogger = 800 ÷ 160 = 5 m/s. Step 2: Relative speed = 10 − 5 = 5 m/s. Step 3: To be 200 m ahead, the faster jogger must gain 200 m on the slower one. Step 4: Time = 200 ÷ 5 = 40 seconds.

Question 11

Two runners start from the same point on a circular track of 800 metres. Runner P runs at 16 m/s and Runner Q runs at 12 m/s in the same direction. How many times will P lap Q in 10 minutes?

Accepted Answer

Step 1: Relative speed = 16 - 12 = 4 m/s. Step 2: In 10 minutes (600 seconds), the relative distance covered = 4 × 600 = 2400 metres. Step 3: Number of laps = 2400 ÷ 800 = 3 laps.

Question 12

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. 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, their relative speed = 12 + 18 = 30 m/s. Step 2: For the first meeting, they together cover the full circumference = 600 m. Step 3: Time = Distance ÷ Relative Speed = 600 ÷ 30 = 20 seconds.

Question 13

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 of A with respect to B = 8 - 6 = 2 m/s. Step 2: For A to lap B, A must cover one complete extra lap, which is 400 metres. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 14

A runner completes one lap of a circular track in 40 seconds. Another runner completes the same lap in 50 seconds. If both start together from the same point in the same direction, how many seconds will elapse before the faster runner is exactly 2 laps ahead of the slower runner?

Accepted Answer

Step 1: In 1 second, faster runner covers 1/40 of the track and slower runner covers 1/50 of the track. Step 2: Relative progress per second = 1/40 - 1/50 = (5 - 4)/200 = 1/200 of the track. Step 3: To be 2 laps ahead, the faster runner must gain 2 complete track lengths. Step 4: Time = 2 ÷ (1/200) = 2 × 200 = 400 seconds.

Question 15

Two runners, A and B, start running on a circular track of length 400 m 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: For A to lap B, A must gain one complete 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 16

Two runners, A and B, start running on a circular track of length 400 m 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 (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 m relative distance. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 17

Two athletes start from the same point on a circular track of 300 m and run in the same direction. Athlete X runs at 6 m/s and Athlete Y runs at 4 m/s. How many seconds after the start will X be exactly one lap ahead of Y?

Accepted Answer

Step 1: For X to be one lap ahead, X must gain 300 m on Y. Step 2: Relative speed = 6 − 4 = 2 m/s. Step 3: Time = Distance ÷ Relative Speed = 300 ÷ 2 = 150 seconds.

Question 18

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. How far ahead (in metres) will A be when they meet for the second time?

Accepted Answer

Step 1: For the second meeting on a circular track (same direction), A must gain exactly 2 laps on B. Distance to gain = 2 × 1200 = 2400 m. Step 2: Relative speed = 15 − 9 = 6 m/s. Step 3: Time for second meeting = 2400 ÷ 6 = 400 seconds. Step 4: At the instant of meeting, both runners are at the same position on the track. Distance of A from starting point = 15 × 400 = 6000 m. Position on track = 6000 mod 1200 = 0 m (i.e., back at the starting point). Therefore, when they meet for the second time, A is 0 m ahead (they are at the same location).

Question 19

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: When moving towards each other on a circular track, relative speed = 12 + 18 = 30 m/s. Step 2: Time to first meeting = 600 / 30 = 20 seconds. Step 3: In 10 minutes (600 seconds), number of meetings = 600 / 20 = 30 times.

Question 20

Two joggers start from the same point on a circular track of length 800 m. Jogger X runs at 6 m/s and Jogger Y runs at 4 m/s, both 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 X to lap Y once = 800 / 2 = 400 seconds. Step 3: Total time = 20 minutes = 1200 seconds. Step 4: Number of laps = 1200 / 400 = 3 times.

Question 21

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 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 to first meeting = 600 / 20 = 30 seconds. Step 3: In 5 minutes (300 seconds), number of meetings = 300 / 30 = 10 times.

RRB NTPC Circular Track & Meeting

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