Let speed of Rajdhani train = $$x$$ km/hr and Express train = $$y$$ km/hr Using, time = distance/speed Acc. to ques, => $$frac{708}{y} - frac{708}{x} = 6$$ => $$frac{1}{y} - frac{1}{x} = frac{6}{708} = frac{1}{118}$$ ----------------(i) If speed of express train is doubled = $$2y$$ km/hr => $$frac{708}{x} - frac{708}{2y} = 3$$ => $$frac{1}{x} - frac{1}{2y} = frac{3}{708} = frac{1}{236}$$ ----------------(ii) Adding equations (i) and (ii), we get : => $$frac{1}{y} - frac{1}{2y} = frac{1}{118} + frac{1}{236}$$ => $$frac{1}{2y} = frac{3}{236}$$ => $$y = frac{118}{3}$$ km/hr $$ herefore$$ Speed of Rajdhani = $$frac{1}{x} = frac{3}{118} - frac{1}{118}$$ => $$frac{1}{x} = frac{2}{118} = frac{1}{59}$$ => $$x = 59$$ km/hr