Let speed of Rajdhani train = $$x$$ km/hr and Express train = $$y$$ km/hr Using, time = distance/speed Acc. to ques, => $$frac{780}{y} - frac{780}{x} = 8$$ => $$frac{1}{y} - frac{1}{x} = frac{8}{780} = frac{2}{195}$$ ----------------(i) If speed of express train is doubled = $$2y$$ km/hr => $$frac{780}{x} - frac{780}{2y} = 6$$ => $$frac{1}{x} - frac{1}{2y} = frac{6}{780} = frac{1}{130}$$ ----------------(ii) Adding equations (i) and (ii), we get : => $$frac{1}{y} - frac{1}{2y} = frac{2}{195} + frac{1}{130}$$ => $$frac{1}{2y} = frac{4 + 3}{390} = frac{7}{390}$$ => $$y = frac{195}{7}$$ km/hr $$ herefore$$ Speed of Rajdhani = $$frac{1}{x} = frac{7}{195} - frac{2}{195}$$ => $$frac{1}{x} = frac{5}{195} = frac{1}{39}$$ => $$x = 39$$ km/hr => Ans - (A)