Question

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

Answer 1

let you travel 1 km at 1km/h speed. So you will take 1km/ 1km/h = 1h.

if you have to take 20% less time,
20% of 1h = 0.2 h
So you will take = 1 - 0.2 = 0.8h

speed = 1km / 0.8h = 1.25 km/h
increase in speed = 1.25 - 1 = 0.25 km/h
% increase = (0.25/1) * 100 = 25%

So you have to increase speed by 25%. 

Answer 2

Let the initial speed be=s kmph Initial time=t h Distance=d km so,s=d/t 20% of t=(20/100)xt=t/5 so,Decrease in t's value=t-(t/5)=4t/5 Now,s=d/(4t/5)=5d/4t=1.25x(d/t) as d/t=s, we can write, s's new value=1.25s Increase in s's value=1.25s-s=0.25s=s/4 so, Increased %={(s/4)x100}/s%=(sx100)/(sx4)%=25%. So, the speed should be increased by 25% to decrease the time by 20%.