Time and Distance has been a regular occurrence in all CAT previous year paper. While the importance given to this topic in CAT syllabus has come down, you can definitely expect at least 1 question from this topic. The best advantage of preparing for Time & Distance is that with a good CAT Preparation, you can be sure of getting the answer right in a short time in the exam. Hence ensure you do more such questions from the 2IIM question bank & other CAT previous years papers to stay on top of this topic.
Question 14 : Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is
The minimum time travelled by Car 1 = 6 hours.
Minimum time travelled by Car 2 = 5 hours
Now, the time taken can be of any value -> (6,5) (7,6) ...... (1000,999)
However, since we want to calculate the highest possible percentage by which speed of car 2 could exceed car 1, we consider the lowest time taken - 6 hours and 5 hours, respectively.
Let the distance between the start and finish be 30 Kms (LCM of 6 and 5)
So, Car 1 travels at 5 Kmph and Car 2 travels at 6 Kmph
Percentage increase in speed by Car 2 = x 100 = x 100 = 20%
The question is "Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is "
Choice A is the correct answer.
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