Question

A contracter employs 360 men who can finish a certain piece of work in 11 months how many extra men must be employed to complete the job in 9 months

Answer 1

$\boxed{\boxed{\boxed{\bold{\purple{Solution : \longrightarrow}}}}}$

$\bold{Let \: \: the \: \: required \: \: number \: \: of \: \: }\\ \bold{men \: \: be \: \: x.}$

$\bold{According \: \: to \: \: question ,\: \: we \: \: }\\\bold{have}$

$\bold{ \frac{}{ |Number \: \: of \: \: months \: \: |11| \: 9| }} \\ \bold{\frac{}{ |Number \: \: of \: \: men \: \: \: \: \: \: \: |360| x| }} \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}{}$

$\bold{Clearly \: \: less \: \: months \: \: will \: \: take \: \:} \\ \bold{more\: \: men \: \: to \: \: finish \: \: the \: \: work.}$

$\bold{So, \: \: it \: \: is \: \: a \: \: case \: \: of \: \: inverse \: \: }\\ \bold{proportion.}$

$\bold{Now \: \: 11 \times 360 = 9 \times x} \\ \\ \bold{= > 11 \times 360 = 9x} \\ \\\bold{ = > x = \frac{11 \times 360}{9}} \\ \\ \bold{= > x = 440}$

$\bold{Hence, \: \: the \: \: required \: \: number \: \: }\\ \bold{of\:\:men \: \: i s \: \: 440.}$