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