QUESTION

CSAT

Hard

Maths

Prelims 2016

A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the shuttle service?

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Explanation

The total duration of the journey from station A to station B is 42 hours. A train starts from each station at 6 AM daily, meaning each train takes 42 hours to complete the journey. Now, to maintain the shuttle service, there must be a continuous flow of trains between station A and station B, with no gaps. So, we need to determine how many trains will be required to maintain this service.

A train is introduced every day from both stations at 6 AM. The journey of each train lasts 42 hours, meaning the train that departs from one station at 6 AM will reach the destination at 12 PM on the third day. Thus, there should always be a train in transit at any given time, and the number of trains required is equal to the number of 42-hour periods it takes to complete a round trip.

Since the journey is a daily shuttle and we have to consider both directions, the number of trains needed is 3 (1 train starting on the first day, 1 on the second day, and 1 on the third day, covering the 42-hour gap).

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