Question

11 men can dig $6\frac{3}{4}$ metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day?

Answer 1

Let x be the number of men required to dig a trench of 27 metre.

Number of men	11	x
Length (in m)	$\frac{27}{4}$	27

$$\begin{gathered} \mathrm{Since}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{trench}\mathrm{and}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{men}\mathrm{are}\mathrm{in}\mathrm{direct}\mathrm{variation},\mathrm{we}\mathrm{have}: \\ \frac{11}{x}=\frac{27/4}{27} \\ \Rightarrow 11\times 27=x\times \frac{27}{4} \\ \Rightarrow x=\frac{11\times 27\times 4}{27} \\ =44 \\ \mathrm{Thus},44\mathrm{men}\mathrm{will}\mathrm{be}\mathrm{required}\mathrm{to}\mathrm{dig}\mathrm{a}\mathrm{trench}\mathrm{of}27\mathrm{metre}. \end{gathered}$$