Speed time distance Q8

Let original speed of the train be $x$ km/hr.

At this speed the train reaches next station in $\frac{120}{x}$ hours.

Since the speed is decreased by $4$ km/hr i.e. it is now $x-4$ km/hr and time taken is now $1$ hour more than the usual time i.e. now it took $\frac{120}{x}+1$ hours to cover $120$ km at the speed of $x-4$ km/hr.

Using $Speed = \frac{Distance}{time}$ we get

$\large x-4 = \frac{120}{\frac{120}{x}+1}$

$\implies x-4=\frac{120x}{120+x}$

$\implies x^2-4x-480=0$

$\implies (x-24)(x+20)=0$

$x=24$

So the original speed is $24$ km/hr