Question

a train covered A certain distance at a uniform speed if the train would have been 10 km per hour faster it would have taken 2 hours less than the scheduled time and the train was lower by 10 km per hour it would have taken 3 hours more than the scheduled time find the distance covered by the train

Answer 1

Let the speed of the train by x km/hr And the time taken by the train be ‘y’ hrs Distance traveled by the train is x.y = xy Case I If the train would have been 10 km/hr faster, it would have taken 2 hours less than the scheduled time. ⇒ (x + 10) (y - 2) = xy ⇒ -2x + 10y = 20 ⇒ x – 5y = -10 ---------------- (1) Case II If the train were slower by 10 km/hr, it would have taken 3 hours more than the scheduled time ⇒ (x - 10) (y + 3) = xy ⇒ 3x – 10y - 30 = 0 ⇒ 3x – 10y = 30 ----------------(2) Solving the equations (1) and (2), we get y = 12, x = 50 Therefore, the distance of the journey = 50 × 12 = 600 km.