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 i one day?
Solution:
Let x be the number of men required to dig a trench of 27 metre.
Since the length of the trench and the number of men are in direct variation, we have:
$\frac{11}{x}=\frac{27 / 4}{27}$
$\Rightarrow 11 \times 27=x \times \frac{27}{4}$
$\Rightarrow x=\frac{11 \times 27 \times 4}{27}$
$=44$
Thus, 44 men will be required to dig a trench of 27 metre.