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

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The question is from the topic Races. It discusses about two persons racing in a swimming pool and the number of times they meet each other. 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 7: A swimming pool is of length 50 m. A and B enter a 300 m race starting simultaneously at one end of the pool at speeds of 3 m/s and 5 m/s. How many times will they meet while travelling in opposite directions before B completes the race?

  1. Twice
  2. Thrice
  3. Once
  4. 5 Times

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Explanatory Answer

Method of solving this CAT Question from Races: Create a table to understand data better, and see if you can pick a pattern from the tables (Visual representation of Data).

Let us say the pool starts from P and ends at Q. B being the quicker one will reach Q first. B will reach Q after 10 seconds. A will take \\frac{50}{3}\\) = 16.67 seconds to reach Q, so between 10s and 16.67 seconds they meet once.

First, let us have a table where we know times when A, B would be at the end points

(in sec)
Position Time
(in sec)
16.67 Q 10 Q
33.33 P 20 P
50 Q 30 Q
66.67 P 40 P
83.33 Q 50 Q
100 P 60 P

We see that the critical time slots are multiples of 10 seconds and multiples of 16.67 seconds.

So, let us break the time from 0 to 60 seconds into these slots and see in which direction A and B travel.

Time Position A Position B Do they cross?
0 to 10 P to Q P to Q
10 to 16.67 P to Q Q to P Yes
16.67 to 20 Q to P Q to P
20 to 30 Q to P P to Q Yes
30 to 33.33 Q to P Q to P
33.33 to 40 P to Q Q to P Yes
40 to 50 P to Q P to Q
50 to 60 Q to P Q to P

So, the question is, how many times will they meet before B finishes the race?

They cross each other thrice totally. Between 10 and 16.67 seconds for the first time; between 20 and 30 seconds for the second time; and between 33.33 to 40 seconds for the third time.

Hence, they meet 3 times before B finishes the race.

Choice B is the correct answer.


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