To travel 780 km, an Express train takes 8 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 6 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, => $$\frac{780}{y} - \frac{780}{x} = 8$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{8}{780} = \frac{2}{195}$$ ----------------(i)

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

=> $$\frac{780}{x} - \frac{780}{2y} = 6$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{6}{780} = \frac{1}{130}$$ ----------------(ii)

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

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{2}{195} + \frac{1}{130}$$

=> $$\frac{1}{2y} = \frac{4 + 3}{390} = \frac{7}{390}$$

=> $$y = \frac{195}{7}$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{7}{195} - \frac{2}{195}$$

=> $$\frac{1}{x} = \frac{5}{195} = \frac{1}{39}$$

=> $$x = 39$$ km/hr

=> Ans - (A)