Question

A work-force of 420 men with a contractor can finish a certain piece of work in 9 months. How many extra men must he employ to complete the job in 7 months?

Answer 1

Let x be the extra number of men employed to complete the job in 7 months.

Number of men	420	x
Months	9	7

$$\begin{gathered} \mathrm{Since}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{men}\mathrm{hired}\mathrm{and}\mathrm{the}\mathrm{time}\mathrm{required}\mathrm{to}\mathrm{finish}\mathrm{the}\mathrm{piece}\mathrm{of}\mathrm{work}\mathrm{are}\mathrm{in}\mathrm{inverse}\mathrm{variation},\mathrm{we}\mathrm{have}: \\ 420\times 9=7x \\ \Rightarrow x=\frac{420\times 9}{7} \\ =540 \\ \mathrm{Thus},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{extra}\mathrm{men}\mathrm{required}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{job}\mathrm{in}7\mathrm{months}=540-420=120 \end{gathered}$$