A mason employed a certain number of workers to finish constructing a wall in a certain number of days.
Solution 1:
We shall assume that the mason's initial error was due to a misjudgement and that the workers are always productive at a fixed rate.
Let $x,y,p$ be the initial number of workers, the desired completion duration in days, and the required percentage, respectively.
| workers $(w)$ | days $(d)$ | jobs $(j)$ |
|---|---|---|
| $x$ | $\displaystyle\frac54y$ | $1$ |
| $x$ | $\displaystyle\frac p{100}\left(\frac54y\right)$ | $\displaystyle\frac p{100}$ |
| $\displaystyle\frac43x$ | $\displaystyle y-\frac p{100}\left(\frac54y\right)$ | $\displaystyle\frac{100-p}{100}$ |
Due to the joint proportionality among $w,d$ and $j,$ there must be some constant $K$ such that $\displaystyle\frac{w_id_i}{j_i}=K.$
Thus, $$\frac{x\left(\frac54y\right)}1=\frac{\left(\frac43x\right)\left(y-\frac p{100}\left(\frac54y\right)\right)}{\frac{100-p}{100}}\\p=20.$$