Question

A train covers a distance of 300 km at a uniform speed. If the speed of
the train is increased by 5 km/hour, it takes 2 hours less in the journey.
Find the original speed of the train.
[CBSE 2017, '19]​

Answer 1

Let x km/h be the constant speed of train.

       Time taken to cover 300km =  300 / x  hrs  

        Increased speed = x + 5

Time taken to cover 300km when speed is increased to 5 km/h  =  300 / x + 5

According to question  

300 / x   -   300 / x + 5  = 2

300( x + 5)  - 300x  /  x(x + 5) = 2

 

300x + 1500 - 300x  /  x2 + 5x = 2

2(x2 + 5) = 1500

2x2 + 10 = 1500

2x2 + 10 - 1500 = 0

2x2 + 10 - 1500 = 0  

(divide by 2 )

x2 + 5 - 750 = 0

30 x -25 = -750

30 + -25 =  5

x2 + 30x - 25x - 750 = 0

x(x + 30) - 25(x + 30) = 0

(x + 30) (x - 25) = 0

x = -30  ( It is rejected because speed cannot be negative )

So , constant speed be  25 km/h

CHEERS !

HOPE IT HELPS