But soon he realized that the work would get delayed by ΒΌ of the time. He then increased the number of workers by a third and they managed to finish the work on schedule. What percentage of the work had been finished by the time the new labor joined?
I know this is the most hated part here at SE, but please provide some hints to begin with such problems. If the workers were 3K, and they took 4 days to complete the work, total units of work would have been 12K. Now, when mason realizes it will take 1 day more, what exactly is that point when he realizes this, so that I can compute what percentage of work was done till then.
Best Answer
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.
The joint proportionality among $w,d$ and $j,$ is such that $\displaystyle\frac{w_id_i}{j_i}$ has a fixed value.
Thus, $$\frac{x\left(\frac54y\right)}1=\frac{\left(\frac43x\right)\left(y-\frac p{100}\left(\frac54y\right)\right)}{\frac{100-p}{100}}\\p=20.$$