A minibus takes 6 hour less to cover 1680 km distance, if its speed is increased by 14 kmph ? What is the usual time of the minibus ?

Answer: Option D

Let
Usual Speed = x kmph.
Now,
Speed of bus after increasing the speed = (x + 14)kmph. . . . . . . (1)
A ____________1680km ____________B
In first case,
Time taken to covered the distance 1680 km = $$\frac{1680}{x}$$ . . . . . . . (2)
In Second Case,
Time Taken to covered the distance 1680 km = $$\frac{1680}{x+14}$$
Time difference = 6 Hours.
So,
$$\begin{array}{rl}& \Rightarrow \frac{1680}{x}-\frac{1680}{x+14}=6\\ & \Rightarrow 1680\frac{14}{x^2+14x}=6\\ & \Rightarrow 280\times 14=x^2+14x\\ & \Rightarrow x^2+70x-56x-3920=0\\ & \Rightarrow x\left(x+70\right)-56\left(x+70\right)=0\\ & \Rightarrow x=-70,56.\\ & \text{hence,}\text{speed}\text{of}\text{minibus}\text{is}56km/h\\ & \text{put}x=56\text{in}\text{equation}(2)\\ & T=\frac{1680}{56}\\ & =30\text{hours}\end{array}$$