To travel 612 km, an Express train takes 9 hours more than Rajdhani. If the speed of the Express train is doubled, it takes 3 hours less than Rajdhani. The speed (in km/hr) of Rajdhani is

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

Using, time = distance/speed

Acc. to ques, => $$\frac{612}{y} - \frac{612}{x} = 9$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{9}{612} = \frac{1}{68}$$ ----------------(i)

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

=> $$\frac{612}{x} - \frac{612}{2y} = 3$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{3}{612} = \frac{1}{204}$$ ----------------(ii)

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

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{1}{68} + \frac{1}{204}$$

=> $$\frac{1}{2y} = \frac{4}{204}$$

=> $$y = \frac{102}{4} = \frac{51}{2}$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{2}{51} - \frac{1}{68}$$

=> $$\frac{1}{x} = \frac{1}{17} \times \frac{5}{12}$$

=> $$x = \frac{204}{5} = 40.8$$ km/hr