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?

- Twice
- Thrice
- Once
- 5 Times

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.

Choice B is the correct answer.

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