CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

CAT Questions

The question is from the topic Circular races. It also involves the idea of relative speed. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 9: A and B stand at distinct points of a circular race track of length 120m. They run at speeds of a m/s and b m/s respectively. They meet for the first time 16 seconds after they start the race and for the second time 40 seconds from the time they start the race. Now, if B had started in the opposite direction to the one he had originally started, they would have meet for the first time after 40 seconds. If B is quicker than A, find B’s speed.

1. 3 m/s
2. 4 m/s
3. 5 m/s
4. 8 m/s

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Races: This is practically just a logical reasoning question.

They meet for the first time 16 seconds after they start the race and for the second time 40 seconds from the time they start the race.
Now, we do not know their relative positions when they start the race. But we know that the time between the first and second meeting is 24 seconds. This is the time when they cover a relative distance of one lap length.

\\frac{Laplength}{RelativeSpeed}\\) = 24; or relative speed = 5 m/s.

The question says – Now, if B had started in the opposite direction to the one he had originally started, they would have met for the first time after 40 seconds.

Now, B would have crossed each other after 40 seconds if B had reversed direction. This is higher than the 24 seconds it takes them to cover the relative distance of a lap in the first instance.
Or, in the first instance they were travelling towards each other.
Or, a + b = 5 m/s.
They meet for the first time 16 seconds after they start the race.

The question is "If B is quicker than A, find B’s speed."

Hence, the answer is 3 m/s

Choice A is the correct answer.