The average speed of a train in the onward journey is 25% more than that of the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is 17 hours covering a distance of 800 km. T

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Q: 134 (IAS/1999)
The average speed of a train in the onward journey is 25% more than that of the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is 17 hours covering a distance of 800 km. The speed of the train in the onward journey is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,2,10,3,3,4,2

keywords: 

{'average speed': [0, 2, 4, 2], 'onward journey': [0, 2, 0, 0], 'speed': [0, 1, 2, 0], 'train': [0, 1, 6, 2], 'return journey': [0, 1, 1, 0], 'train halts': [0, 1, 0, 0], 'total time': [0, 0, 2, 0], 'km': [0, 0, 2, 1], 'distance': [0, 3, 3, 3], 'journey': [0, 1, 3, 2], 'hour': [5, 5, 11, 12], 'hours': [7, 2, 16, 9], 'destination': [0, 2, 2, 3]}

The question provides that the average speed of the train on the onward journey is 25% more than that of the return journey. Let`s denote the speed of the train during the return journey as `v` km/h. Then, the speed during the onward journey will be 1.25v km/h due to the mentioned 25% increase.

The total distance covered is 800 km which means 400 km each for onward and return journeys. Therefore, the total journey time can be calculated as onward journey duration (400 km / 1.25v hours) plus return journey duration (400 km /v hours) plus halt time (1 hour). The total time taken for the complete journey is already given as 17 hours.

In option 1, if we put the speed as 45 km/h, the total duration results more than given 17 hours. Similarly, for option 2 and option 3.

In option 4, if we put the speed as 56.25 km/h, the total duration exactly results as given 17 hours. Thus, the speed of the train in onward journey is 56.25 km per hour.