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The average speed of a train is 20% less on the return journey than on onward journey. The train halts for half an hour at the destination station before starting on the return journey. If the total time taken for the to and fro journey is 23 hours, covering a distance of 1000 km, the speed of the train on the return journey is:

The average speed of a train is 20% less on the return journey than on onward journey. The train halts for half an hour at the destination station before starting on the return journey. If the total time taken for the to and fro journey is 23 hours, covering a distance of 1000 km, the speed of the train on the return journey is: Correct Answer 40 km/hr

Train was halted for half an hourSo, total time taken in Journey = 23 - $$\frac{1}{2}$$ = 22.5 hoursAverage speed in Whole Journey = $$\frac{{1000}}{{22.5}}$$  = 44.5 km/hrThe average speed on return journey is 20% less than onward journey.Therefore, ratio of average speed of onward and return journey,$$\eqalign{ & = \frac{{100}}{{80}} \cr & = \frac{5}{4} \cr} $$Let average speed of onward journey = 5xAverage speed on return journey = 4xAverage speed on whole journey = $$\frac{{5x + 4x}}{2}$$44.5 = $$\frac{{5x + 4x}}{2}$$89 = 9xx = 9.88Average speed on return
= 9.88 × 4
= 39.52
= 40 km/hr (Approx.)

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