To travel 732 km, an Express train takes 6 hours more than Rajdhani. If the speed of the Express train is doubled, it takes 3 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, => $$\frac{732}{y} - \frac{732}{x} = 6$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{6}{732} = \frac{1}{122}$$ ----------------(i)

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

=> $$\frac{732}{x} - \frac{732}{2y} = 3$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{3}{732} = \frac{1}{244}$$ ----------------(ii)

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

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{1}{122} + \frac{1}{244}$$

=> $$\frac{1}{2y} = \frac{3}{244}$$

=> $$y = \frac{122}{3}$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{3}{122} - \frac{1}{122}$$

=> $$\frac{1}{x} = \frac{2}{122} = \frac{1}{61}$$

=> $$x = 61$$ km/hr