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 $27$ meter.

Number of men	$11$	$x$
Length ( in m )	$6\frac{3}{4}=\frac{27}{4}$	$27$

Since, the length of the trench and the number of men are in direct variation, we have:

$\Rightarrow$ $\frac{11}{x}=\frac{27/4}{27}$

$\Rightarrow$ $11\times 27=x\times \frac{27}{4}$

$\Rightarrow$ $x=\frac{11\times 27\times 4}{27}$

$\Rightarrow$ $x=44$

$\therefore$ $44$ men will be required to dig a trench of $27$ meter.