By how much percent must a motorist increase his speed in order of reduce by 20%, the time taken to cover a certain distance ?

Answer: Option B

Let the distance be x km and the original time time taken be y hours.
Then,
Original speed = $$\frac{x}{y}$$ km/hr
New speed :
$$\begin{array}{rl}& =\left(\frac{x}{80\%\text{ of }y}\right)\text{ km/hr}\\ & =\left(\frac{5}{4}.\frac{x}{y}\right)\text{ km/hr}\end{array}$$
Increase in speed :
$$\begin{array}{rl}& \text{ = }\left(\frac{5x}{4y}-\frac{x}{y}\right)\\ & \text{ = }\frac{x}{4y}\end{array}$$
∴ Increase %
$$\begin{array}{rl}& \text{ = }\left(\frac{x}{4y}\times \frac{y}{x}\times 100\right)\%\\ & =25\%\end{array}$$