To travel 648 km, an Express train takes 12 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 6 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, => $$\frac{648}{y} - \frac{648}{x} = 12$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{12}{648} = \frac{1}{54}$$ ----------------(i)

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

=> $$\frac{648}{x} - \frac{648}{2y} = 6$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{6}{648} = \frac{1}{108}$$ ----------------(ii)

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

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{1}{54} + \frac{1}{108}$$

=> $$\frac{1}{2y} = \frac{3}{108}$$

=> $$y = \frac{108}{6} = 18$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{1}{18} - \frac{1}{54}$$

=> $$\frac{1}{x} = \frac{2}{54} = \frac{1}{27}$$

=> $$x = 27$$ km/hr