Question

a train covers a distance of 300 km at a uniform speed if the speed of the train increased by 5 kilometre per hour it takes two hour less i the journey find the original speed

Answer 1

HEY DEAR ...

Total distance=300km
let speed=xkm/hr
therefore time = d/s = 300/x hr---------------1
new speed=x+5 km/hr
therefore time=d/s = 300/x+5 hr-------------2
given difference in times = 2 hrs
therefore from 1 and 2
300/x - 300/x+5 = 2
300x+1500-300x/x(x+5) = 2
1500 = 2xsquare + 10x
2x square + 10x - 1500 = 0
x2 + 5x - 750 = 0
x2 + 30x - 25x -750 =0
x(x+30) - 25(x+30)
(x+30)(x-25)=0
x+30=0  !     x-25=0    
x= -30    !      x = 25
 speed cannot be measured in negetive
therefore original speed of train is 25 km/hr

HOPE , IT HELPS ...

Answer 2

Let the usual speed of the train be x km/h

300/x –300/x+5=2

⇒ x² + 5x – 750 = 0

⇒ (x + 30) (x – 25) = 0

⇒ x = – 30, 25

\ Usual Speed of the train = 25 km/h