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

Solution(By Examveda Team)

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 :
$$\eqalign{ & = \left( {\frac{x}{{80\% {\text{ of }}y}}} \right){\text{ km/hr}} \cr & = \left( {\frac{5}{4}.\frac{x}{y}} \right){\text{ km/hr}} \cr} $$
Increase in speed :
$$\eqalign{ & {\text{ = }}\left( {\frac{{5x}}{{4y}} - \frac{x}{y}} \right) \cr & {\text{ = }}\frac{x}{{4y}} \cr} $$
∴ Increase %
$$\eqalign{ & {\text{ = }}\left( {\frac{x}{{4y}} \times \frac{y}{x} \times 100} \right)\% \cr & = 25\% \cr} $$