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CAT Previous Year Paper | CAT Quants Questions | Question 13

This question is about circular races. Time Speed Distance and Races is one of the most heavily tested topics in the CAT Exam and appears more often than expected in the CAT Exam. This topic is very interesting as it is relatable to real-life scenarios. Races as an idea is built on CAT Speed time distance, Ratio proportions. One can usually expect 3-4 questions from these ideas in the CAT exam .

Question 13 : Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

  1. 4.6
  2. 4.2
  3. 4.8
  4. 5.2

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Explanatory Answer

We are given the individual speeds of Anil, Sunil and Ravi, which are 15 kmph, 10 kmph and 8 kmph respectively.
We are also told that the length of the track is 3 KM.

Let us calculate the time taken by Anil and Sunil to complete one round(which is 3KM in length):
Time taken by Anil to complete one round in minutes = \\frac{Length of the track in km}{Anil's speed in kmph}) × 60 minutes = \\frac{3}{15}) × 60 = 12 minutes.
Time taken by Sunil to complete one round in minutes = \\frac{Length of the track in km}{Sunil's speed in kmph}) × 60 minutes = \\frac{3}{10}) × 60 = 18 minutes.

Anil completing each round in 12 minutes, reaches the starting point at 12, 24, 36, 48, 60 .... minutes
Sunil completing each round in 18 minutes, reaches the starting point at 18, 36, 54, 72, 90 .... minutes

Clearly, both of them reach the starting point at 36 minutes, for the first time together.
Observe that 36 is teh LCM of 12 and 18

The distance covered by Ravi, whose speed is 8 kmph in 36 minutes(or \\frac{36}{60}) = 0.6 hours) = 8 × 0.6 = 4.8 km


The answer is, "4.8"

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