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CAT Previous Year Paper | CAT Quants Questions | Question 21

This question is from Speed time distance. Speed time distance is one of the heavily tested topics in the CAT Exam. Questions from this topic have consistently appeared in every edition of the CAT exams. You can expect 2-3 questions from this topic in the CAT Exam. Make sure a get a good hold on this topic by practicing tons of CAT Level Questions. Worried about where to find questions to practice? Check out 2IIM CAT Question Bank to practice 1000+ CAT level questions with detailed video and text solutions for free.

Question 21 : A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

  1. 11 : 20 am
  2. 11 : 00 am
  3. 10 : 45 am
  4. 11 : 45 am

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Explanatory Answer

Let's represent the positions of the trains at 9:00 AM
Train Positions at 9:00 AM
Train from station B will not start till 10:30 AM, meanwhile train A starts from A at 9:00 AM, and travels for 1.5 hours at 40kmph speed. Therefore, by 10:30 AM, train A travels 1.5 × 40 = 60 km towards B.

The positions of the two trains at 10:30 AM will be
Train Positions at 9:00 AM
Now both the trains A and B have 90 - 60 = 30 km to cover between them.
The relative speed of the two trains will be 40 + 20 = 60kmph.
With a relative speed of 60kmph, the two trains cover 30km in half an hour.
Hence the two trains will meet at 11: 00 AM

The answer is, "11 : 00 am"

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