To travel 816 km, an Express train takes 9 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 4 hours less than Rajdhani. What is the speed of Rajdhani?

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

Using, time = distance/speed

Acc. to ques, => $$\frac{816}{y} - \frac{816}{x} = 9$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{9}{816} = \frac{3}{272}$$ ----------------(i)

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

=> $$\frac{816}{x} - \frac{816}{2y} = 4$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{4}{816} = \frac{1}{204}$$ ----------------(ii)

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

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{3}{272} + \frac{1}{204}$$

=> $$\frac{1}{2y} = \frac{9 + 4}{816}$$

=> $$y = \frac{408}{13}$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{13}{408} - \frac{3}{272}$$

=> $$\frac{1}{x} = \frac{26 - 9}{816} = \frac{17}{816}$$

=> $$x = \frac{816}{17} = 48$$ km/hr