To travel 672 km, an Express train takes 14 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 8 hours less than Rajdhani. The speed of Rajdhani is

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

Using, time = distance/speed

Acc. to ques, => $$\frac{672}{y} - \frac{672}{x} = 14$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{14}{672} = \frac{1}{48}$$ ----------------(i)

If speed of express train is doubled = $$2y$$ km/hr

=> $$\frac{672}{x} - \frac{672}{2y} = 8$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{8}{672} = \frac{1}{84}$$ ----------------(ii)

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

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{1}{48} + \frac{1}{84}$$

=> $$\frac{1}{2y} = \frac{11}{336}$$

=> $$y = \frac{168}{11}$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{11}{168} - \frac{1}{48}$$

=> $$\frac{1}{x} = \frac{11 - 3.5}{168} = \frac{7.5}{168}$$

=> $$x = \frac{168}{7.5} = 22.4$$ km/hr