To travel 432 km, an Express train takes 1 hour more than Duronto. If however, the speed of the Express train is increased by 50%, it takes 2 hours less than Duronto. What is the speed (in km/hr) of Duronto train?

Let speed of Duronto train = $$x$$ km/hr and Express train = $$y$$ km/hr

Using, time = distance/speed

Acc. to ques, => $$\frac{432}{y} - \frac{432}{x} = 1$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{1}{432}$$ ----------------(i)

If speed of express train is increased by 50% = $$1.5y$$ km/hr

=> $$\frac{432}{x} - \frac{432}{1.5y} = 2$$

=> $$\frac{1}{x} - \frac{1}{1.5y} = \frac{2}{432}$$ ----------------(ii)

Adding equations (i) and (ii), we get :

=> $$\frac{1}{y} - \frac{1}{1.5y} = \frac{1}{432} + \frac{2}{432}$$

=> $$\frac{1}{3y} = \frac{3}{432}$$

=> $$y = \frac{1}{3}\times\frac{432}{3} = 48$$ km/hr

$$\therefore$$ Speed of Duronto (in equation (i)) = $$\frac{1}{x} = \frac{1}{48} - \frac{1}{432}$$

=> $$\frac{1}{x} = \frac{9-1}{432} = \frac{8}{432}$$

=> $$x = 54$$ km/hr

=> Ans - (B)