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

CAT Questions

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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Video Explanation

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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

A		B
Time (in sec)	Position	Time (in sec)	Position
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.