Calculating overtaking instances on a circular track with relative speeds
Question
X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
Options
2
3
4
5
Explanation
First, calculate the total number of rounds required to finish the race: Total rounds = 3000 m / 300 m = 10 rounds.
The speed ratio of X to Y is 3:2. This implies that for every 3 rounds X runs, Y runs exactly 2 rounds. A faster runner overtakes a slower runner on a circular track every time they complete exactly 1 more full lap than the slower runner.
Let's map X's progress to the overtaking points:
X finishes the 10-round race before reaching the 12th round milestone necessary for a 4th overtake. Therefore, X passes Y exactly 3 times.
Answer: (b).
Question details
Year
2022
Paper
CSAT
Question
Q15
Section
Numerical Ability
Sub-topic
Time, Speed & Distance
Type
Factual single
Difficulty
Hard
Source hint
X and Y run a 3 km race on 300m track
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