To travel 648 km, an Express train takes 12 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 6 hou…

is 27 km/hr is the correct answer?? am i right?

Yes 27k/h is the right answer

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

Using, time = distance/speed

Acc. to ques, $= \frac{648}{y} - \frac{648}{x} = 12$

$= \frac{1}{y} - \frac{1}{x} = \frac{12}{648} = \frac{1}{54}$ ----------------(i)

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

$= \frac{648}{x} - \frac{648}{2y} = 6$

$= \frac{1}{x} - \frac{1}{2y} = \frac{6}{648} = \frac{1}{108}$ ----------------(ii)

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

$= \frac{1}{y} - \frac{1}{2y} = \frac{1}{54} + \frac{1}{108}$

$= \frac{1}{2y} = \frac{3}{108}$

$= y = \frac{108}{6} = 18 km/hr$

$\therefore Speed of Rajdhani = \frac{1}{x} = \frac{1}{18} - \frac{1}{54}$

$= \frac{1}{x} = \frac{2}{54} = \frac{1}{27}$

$= x = 27$ km/hrTo travel $648$ km, an Express train takes $12$ hours more than Rajdhani.