1. 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 hours less than Rajdhani. The speed of Rajdhani is _____.
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By: anil on 05 May 2019 02.12 am
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 $$ herefore$$ Speed of Rajdhani = $$frac{1}{x} = frac{1}{18} - frac{1}{54}$$ => $$frac{1}{x} = frac{2}{54} = frac{1}{27}$$ => $$x = 27$$ km/hr
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