(Q26) A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

The distancce travelled = 360 km.

Let the speed of the train = x kmph.

Time taken to complete a journey =
distance
speed

By problem
360
x
 -
360
x+5
 = 1

360(
1
x
 -
1
x+5
)=1

360(
x+5-x
x(x+5)
)=1

x2+5x
 =
1
360

x2 + 5x =

x2 + 5x - = 0

x2 + 45x - x - = 0

x(x + 45) - (x + 45)

(x + 45)(x - ) = 0

x + 45 = 0 or x - = 0

x = -45 or x =

But x can't be negative.

∴ The speed of the train = kmph.