To travel 660 km, an Express train takes 10 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 7 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, => $$\frac{660}{y} - \frac{660}{x} = 10$$

=> $$\frac{1}{y} - \frac{1}{x} = \frac{10}{660} = \frac{1}{66}$$ ----------------(i)

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

=> $$\frac{660}{x} - \frac{660}{2y} = 7$$

=> $$\frac{1}{x} - \frac{1}{2y} = \frac{7}{660}$$ ----------------(ii)

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

=> $$\frac{1}{y} - \frac{1}{2y} = \frac{1}{66} + \frac{7}{660}$$

=> $$\frac{1}{2y} = \frac{17}{660}$$

=> $$y = \frac{330}{17}$$ km/hr

$$\therefore$$ Speed of Rajdhani = $$\frac{1}{x} = \frac{17}{330} - \frac{1}{66}$$

=> $$\frac{1}{x} = \frac{17-5}{330} = \frac{12}{330} = \frac{2}{55}$$

=> $$x = 27.5$$ km/hr

=> Ans - (D)