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

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

$\bold\red{360 \: \: men \: \: can \: \: finish \: \: the \: \: work }\\ \bold{in \: \: 11\: \: months.}$

$\bold\purple{Let \: \: y \: \: men \: \:can\: \: finish \: \: the \: \: work} \\ \bold{in \: \: 9 \: \: months.}$

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

$\bold\red{\frac{}{ | Number \: \: of \: \: men \: \: \: \: \: \: | \: 360 \: | \: y \: | }} \\ \bold\pink{ \frac{}{ |Number \: \: of \: \: months| \: 11 \: \: \: \: |9 \: | } }\\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}$

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

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

$\bold{Now, \: \: 360 \times 11 = y \times 9} \\ \\ \bold{= > 360 \times 11 = 9y} \\ \\ \bold{= > y = \frac{11 \times 360}{9}} \\ \\ \bold{= > y = 440.}$

$\bold\green{Hence, \: \: 440 \: \: men \: \: can \: \: finish}\\\bold\green{ the \: \:work\: \: in \: \: 9 \: \: months.}$