By how much percent must a motorist increase his speed in order to reduce by 20\%, the time taken to cover a certain distance?
(a)20
(b)25
(c)30
(d)35
Answer
Answer (as printed): B
Explanation
Let the distance be $x \mathrm{km}$ and the original time taken be $y$ hours. Then, Original speed $=\left(\frac{x}{y}\right) \mathrm{km} / \mathrm{hr}$. New speed $=\left(\frac{x}{80 \% \text { of } y}\right) \mathrm{km} / \mathrm{hr}=\left(\frac{5}{4} \cdot \frac{x}{y}\right) \mathrm{km} / \mathrm{hr}$. Increase in speed $=\left(\frac{5 x}{4 y}-\frac{x}{y}\right)=\frac{x}{4 y}$. ∴ Increase $\%=\left(\frac{x}{4 y} \times \frac{y}{x} \times 100\right) \%=25 \%$.