Let speed of Duronto train = $$x$$ km/hr and Express train = $$y$$ km/hr Using, time = distance/speed Acc. to ques, => $$frac{432}{y} - frac{432}{x} = 1$$ => $$frac{1}{y} - frac{1}{x} = frac{1}{432}$$ ----------------(i) If speed of express train is increased by 50% = $$1.5y$$ km/hr => $$frac{432}{x} - frac{432}{1.5y} = 2$$ => $$frac{1}{x} - frac{1}{1.5y} = frac{2}{432}$$ ----------------(ii) Adding equations (i) and (ii), we get : => $$frac{1}{y} - frac{1}{1.5y} = frac{1}{432} + frac{2}{432}$$ => $$frac{1}{3y} = frac{3}{432}$$ => $$y = frac{1}{3} imesfrac{432}{3} = 48$$ km/hr $$ herefore$$ Speed of Duronto (in equation (i)) = $$frac{1}{x} = frac{1}{48} - frac{1}{432}$$ => $$frac{1}{x} = frac{9-1}{432} = frac{8}{432}$$ => $$x = 54$$ km/hr => Ans - (B)