Practice Questions
Concept Explanation
On a circular track, runners meet when the relative distance covered equals the track length (same direction) or when combined distance equals one lap (opposite direction).
Key Formulas
- Same direction, first meeting: Time = Circumference / |a − b|
- Opposite direction, first meeting: Time = Circumference / (a + b)
- Number of meetings in time t (same direction) = (relative distance)/C
Example
Track 300 m. A at 5 m/s, B at 3 m/s same direction. First meeting in 300/(5−3) = 150 s.
Common Trap
Same-direction meetings need relative speed, not sum of speeds.
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Q1 Medium
Two runners A and B start together from the same point on a circular track of circumference 300 metres and run in the same direction at 5 m/s and 3 m/s respectively. After how many seconds will they meet for the first time?
ExplanationRelative = 2 m/s. Time = 300/2 = 150 s. -
Q2 Medium
On a circular track of 400 metres, A and B start from the same point and run in opposite directions at 6 m/s and 4 m/s respectively. After how many seconds will they meet for the first time?
ExplanationRelative = 10 m/s. Time = 400/10 = 40 s. -
Q3 Easy
Two runners start from the same point on a circular track of 500 metres and run in opposite directions, each at 10 m/s. After how many seconds will they meet for the first time?
ExplanationRelative = 20 m/s. Time = 500/20 = 25 s. -
Q4 Hard
On a circular track of 240 metres, A runs at 6 m/s and B runs at 2 m/s in the same direction, starting together. How many times will they meet during a period of 2 minutes?
ExplanationRelative = 4 m/s. In 120 s, relative distance = 480 m = 2 laps ⇒ 2 meetings. -
Q5 Hard
Two runners A and B start together on a 240 metre circular track and run in the same direction at 5 m/s and 3 m/s respectively. How many times will they meet during 120 seconds?
ExplanationRelative distance = 2 × 120 = 240 m = one lap ⇒ 1 meeting. -
Q6 Medium
A and B start from the same point on a circular track of 240 metres and run in the same direction at 5 m/s and 3 m/s respectively. After how many seconds will they meet for the first time?
ExplanationRelative = 2 m/s. Time = 240/2 = 120 s. -
Q7 Easy
On a circular track of 600 metres, A and B start together and run in opposite directions at 8 m/s and 4 m/s respectively. After how many seconds will they meet for the first time?
ExplanationRelative = 12 m/s. Time = 600/12 = 50 s.
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Q8 Easy
Two runners start from the same point on a circular track of 450 metres and run in opposite directions, each at 9 m/s. After how many seconds will they meet for the first time?
ExplanationRelative = 18 m/s. Time = 450/18 = 25 s. -
Q9 Medium
On a circular track of 300 metres, A runs at 6 m/s and B runs at 2 m/s in the same direction, starting from the same point. After how many seconds will A overtake B for the first time?
ExplanationRelative = 4 m/s. Time = 300/4 = 75 s. -
Q10 Medium
On an 800 metre circular track, A runs at 10 m/s and B runs at 6 m/s in the same direction, starting together. How often do they meet?
ExplanationTime between meetings = 800/4 = 200 s. -
Q11 Easy
Two runners start from the same point on a 500 metre circular track and run in opposite directions at 15 m/s and 10 m/s respectively. After how many seconds will they meet for the first time?
ExplanationRelative = 25 m/s. Time = 500/25 = 20 s. -
Q12 Medium
A and B start together on a circular track of 420 metres and run in the same direction at 7 m/s and 4 m/s respectively. After how many seconds will they meet for the first time?
ExplanationRelative = 3 m/s. Time = 420/3 = 140 s. -
Q13 Easy
Two runners start together from the same point on a circular track and run in the same direction at the same constant speed. Which of the following is correct?
ExplanationEqual speeds ⇒ relative speed 0 ⇒ never meet. -
Q14 Medium
On a circular track of 360 metres, A and B start from the same point and run in opposite directions at 9 m/s and 3 m/s respectively. After how many seconds will they meet for the first time?
ExplanationRelative = 12 m/s. Time = 360/12 = 30 s.
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DS1 Medium
Two runners start together on a circular track and run in the same direction. After how many seconds will they meet for the first time?
Statement IThe circumference of the circular track is 300 metres.
Statement IIThe speeds of the two runners are 5 m/s and 3 m/s respectively.
ExplanationRelative = 2 m/s. Time = 300/2 = 150 s. -
DS2 Medium
Two runners start from the same point on a circular track and run in opposite directions. After how many seconds will they meet for the first time?
Statement IThe circumference of the circular track is 400 metres.
Statement IIThe two runners move in opposite directions at 6 m/s and 4 m/s respectively.
ExplanationRelative = 10 m/s. Time = 400/10 = 40 s.
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DS3 Medium
Will the two runners meet for the first time within 100 seconds of starting together?
Statement IOn a 240 metre track, two runners start together and run in the same direction at 5 m/s and 3 m/s respectively.
Statement IIOn a 600 metre track, two runners start together and run in opposite directions at 8 m/s and 4 m/s respectively.
ExplanationI: 240/2 = 120 s, not within 100. II: 600/12 = 50 s, within 100. -
DS4 Easy
What is the relative speed of two runners on a circular track?
Statement ITwo runners move in the same direction at 8 m/s and 5 m/s respectively.
Statement IITwo runners move in opposite directions at 8 m/s and 5 m/s respectively.
ExplanationI alone: |8 − 5| = 3 m/s. II gives 13 m/s.