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 train is _____.
Let the speed of Rajdhani be x km/hr. And the speed of Express train be y km/hr. To travel 648 km, an Express train takes 12 hours more than Rajdhani. So, 648/x = (648/y) -12 ⇒ (648/x) - (648/y) = -12 ----(1) However, the speed of the Express train is doubled, it takes 6 hours less than Rajdhani. So, 648/2y = (648/x) -6 ⇒ (648/x) - (648/2y) = 6 ----(2) Subtracting eq. (2) from eq. (1) we get, ⇒ -(648/y) + (648/2y) = -12 - 6 ⇒ -1296 + 648 = -36y ⇒ 36y = 648 ⇒ y = 18 So, 648/x = (648/18) -12 ⇒ 648/x = 36 - 12 ⇒ x = 27 ∴ The speed of Rajdhani train = 27 km/hr. Short Trick: ∵Speed of Express train is doubled, ∴Time reduces by 1/2 Let ‘t’ be the original time taken by express train. Total time difference = 12 + 6 = 18 hour ⇒½ × t = 18 or t = 36 hours ⇒Rajdhani takes 12 hours less = 36 - 12 = 24 hours to complete the journey. ∴Speed of Rajdhani = 648/24 = 27 km/hour