Question : How much percentage should a racer increase speed to reduce the time by 20% to cover a fixed distance?
Option 1: 25%
Option 2: 30%
Option 3: 40%
Option 4: 35%
Correct Answer: 25%
Solution :
We know,
$\text{Speed}=\frac{\text{Distance}}{{\text{Time}}}$
$\text{Speed}\propto\frac{\text{1}}{{\text{Time}}}$
If the distance remains constant, then speed is inversely proportional to time.
If the time is reduced by 20%, the new time is 80% (or 0.8 times) of the original time.
Since speed is inversely proportional to time, the new speed must be ($\frac{1}{0.8}$) = 1.25 times the original speed to maintain the same distance.
An increase from 1 to 1.25 is an increase of 0.25, or 25% when expressed as a percentage.
Hence, the correct answer is 25%.
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