Question

A train covers 300 kilometre at a uniform speed If the speed had been 5 kilometre an hour more the journey would have taken 2 hours less find the speed of the train

Answer 1

Let the initial speed of the train be - x
Increased speed = x+5
Distance covered in both cases = 300km
Time taken in initial speed = $\frac{300}{x}$ 
Time taken in increased speed = $\frac{300}{x+5}$
Given, Time taken in increased speed = Time taken in initial speed -2 
= $\frac{300}{x+5}$ =  $\frac{300}{x}$ -2
= $\frac{300}{x+5}$ = $\frac{300-2x}{x}$
By cross multiplying
= 300(x) = (300-2x) (x+5)
Just simplify and solve from here as a quadratic equation

Hope this helped
Reagrds
Jai

Answer 2

Let x be the speed of train
Time taken to cover 300 km = 300/x 
Increased speed = x+5
Time taken to cover 300 km when speed is increased to 5 km/hr
= 300/ x+5

According to the question
300/x - 300/ x+5 = 2  ( 2 hrs less )
300(x+5)- 300x / x(x+5)=2
300x + 1500 - 300x / x^2+5x = 2
1500/x^2+5x= 2
2(x^2+5)= 1500
2x^2+10 = 1500
2x^2+10-1500= 0
(divide by 2 )
x^2+5-750=0

Now,
30* -25 = -750 ( 2 multiples if 750)
Also,
30+ -25 = 5

Therefore,
x^2+30x-25x-750=0
x(x+30)- 25(x+30)=0  ( Factorization)
(x+30)(x-25) are the factors

So, we obtain two numbers:
-30 and 25
The speed can't be -30 because negative speed is rejected.
Therefore, the speed has to be 25

So, the constant speed is 25 km/hr