A train takes 45 minutes to cover a certain distance at a speed of 80 km/h. If the speed is increased by 125%, then how long will it take the train to cover $\frac{8}{5}$ of the same distance?

32 minutes 

Distance = Speed × Time

= 80 ×  \(\frac{45 }{60}\)

= 60 km

125 % = \(\frac{5 }{4}\)

Original Speed  :  New Speed

         4            :         9

4R = 80 km/h

R = 20 km/h

New speed , 9R = 9 × 20 = 180 km/h

\(\frac{8 }{5}\)th of distance = 60  × \(\frac{8}{5}\) = 96 km

Time = \(\frac{96}{180}\) × 60

= 32 minutes