In a company there are 75\% skilled workers and the remaining are unskilled. 80\% of skilled workers and 20\% of unskilled workers are permanent. If the number of temporary workers is 126, then what is the total number of workers?
(a)360
(b)377
(c)480
(d)510
Answer
Answer (as printed): A
Explanation
Let the total number of workers be $x$. Then, number of skilled workers $=75 \%$ of $x=\frac{3 x}{4}$. Number of unskilled workers $=\left(x-\frac{3 x}{4}\right)=\frac{x}{4}$. Number of temporary workers $$\begin{aligned} & =(100-80) \% \text { of } \frac{3 x}{4}+(100-20) \% \text { of } \frac{x}{4} \\ & =20 \% \text { of } \frac{3 x}{4}+80 \% \text { of } \frac{x}{4}=\left(\frac{20}{100} \times \frac{3 x}{4}+\frac{80}{100} \times \frac{x}{4}\right)=\frac{7 x}{20} . \\ & \therefore \frac{7 x}{20}=126 \Rightarrow x=\left(\frac{126 \times 20}{7}\right)=360 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.