Speed, Time, Distance : CAT 2016 Math Questions Answers
Question 4 the day : May 19, 2003
The question for the day is from the topic of Time and Distance. The question helps in getting a good grasp on the concept of finding the length of a train given its speed relative to another train.
Question
A passenger train covers the distance between stations X and Y, 50 minutes faster than a goods train. Find this distance if the average speed of the passenger train is 60 kmph and that of goods train is 20 kmph.
 20 kms
 25 kms
 45 kms
 40 kms
Correct Answer is 25 kms. Choice (2) is right.
Explanatory Answer
Let 'd' be the distance between the stations X and Y.
Time taken by the passenger train to cover the distance 'd' = d/60 hour
Time taken by the goods train to cover the distance 'd' = d/20 hour
Time difference between these two trains is given by 50 minutes or 50/60 hour
i.e., (d/20)  (d/60) = 50/60
d = 25kms.
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