Question

Progressive express left for New Delhi, increasing its speed in each hour. It started its journey from Lucknow, but after four hours of its journey, it met with an accident. Its speed in the fourth hour was $\frac{7}{5}$ times that of the third hour and the speed in the third hour was $\frac{10}{7}$ times that of the second hour and in the second hour it was $\frac{7}{5}$ times that of the first hour. If it had travelled with half of the speed of the third hour during the whole time, then it would have gone 160 km less in the same time (i. e. , in four hours). The average speed of the train during the journey of 4 hours was:

• A. 50 km/hr
• B. 90 km/hr
• C. 80 km/hr
• D. can't be determined

Answer 1

The correct option is B 90 km/hr

Let the speed for the first hour be x km/hr
then the speed for the second hour be $\frac{7}{5}x$ km/hr
then the speed for the fourth hour be $2x\times \frac{7}{5}=\frac{14x}{5}km/hr$
Therefore total distance in four hours $x+\frac{7}{5}x+2x+\frac{14x}{5}$
$=\frac{36x}{5}km$
$\therefore$ Average speed $=\frac{TotalDistance}{TotalTime}=\frac{\left(\frac{36x}{5}\right)}{4}=\frac{9x}{5}km/hr$
Again the distance in 4 hours @ speed of x km/hr
which is half of the third hour's speed is 4x km
Hence $\frac{36x}{5}-4x=160km$
$\Rightarrow$ x = 50
Hence, the average speed $=\frac{9\times 50}{5}=90km/hr$