Define Work and Time

Work is defined as something which has an effect or outcome. When it is said that someone has done any work, it means he/she has done \(100 \%\) of the work. Hence, if Ashok finishes his work in 5 days, it means that in 5 days, he will finish \(100 \%\) of the work. Hence, we can say that in 1 day he finishes \(100/5=20 \%\) of the work. Similarly, in 2 days, he finishes \(40 \%\) of the work, and in 4 days, he finishes \(80 \%\) of the work.

When two quantities \(x\) and \(y\) are in direct proportion, both \(x\) and \(y\) increases or decreases at the same rate. When \(x\) increases, \(y\) also increases, keeping the ratio between them constant always.
\(x \propto y\)
Removing the proportionality, we can write this as:
\(x=k y\), where \(k\) is the proportionality constant. \(\Rightarrow \frac{x}{y}=k\)
However, in our daily lives, we come across situations where an increase in one quantity results in a corresponding decrease in another corresponding amount or vice versa. For example, when a motorist travels at a higher speed, the time taken to cover a certain distance is reduced. This is the indirect proportion or indirect variation.
If we consider two quantities \(x\) and \(y\), then when \(x\) increases, \(y\) decreases.
\(x \propto \frac{1}{y}\)
Removing the proportionality, we can write this as \(x y=k\), where \(k\) is the proportionality constant.