The speed of train A is 16 km/h less than the speed of train B. To cover a distance of 384 km, B takes 4 hours less time than A. What is the speed (in km/h) of train B?

Let B speed $$x $$ Km/hr and time taken by A is t hr 

For B      $$x = \dfrac {384}{t-4} $$   

Again for A $$ x-16 = \dfrac {384}{t}$$

we the value of x and solve it

$$\Rightarrow \dfrac {384}{t-4}  - 16 = \dfrac {384}{t}$$

$$\Rightarrow \dfrac {384-16t+ 64}{t-4} = \dfrac {384}{t}$$

$$\Rightarrow 384 t - 16 t^2 + 64 t = 384 t - 384\times 4 $$

$$\Rightarrow 16t^2 - 64t - 1536 = 0 $$

$$\Rightarrow t^2 - 4t - 96 = 0 $$

$$\Rightarrow (t-12)(t+2)= 0 $$

$$\Rightarrow t= 12 , t= - 2 $$

then speed of train B =$$ \dfrac {384} {12-4}$$

$$\Rightarrow \dfrac {384}{8} = 48 $$ km/hr Ans