Question

A certain number of men can do a
work in 40 days. If there were men
5 less it could be finished in
20 days more. How many men are
there?​

Answer 1

Answer:

There are 15 men.

Step-by-step explanation:

Question says that, A certain number of men can do a work in 40 days. If 5 less would be there it could be finished in 20 days more. Find the number of men.

Step 1 : Let's assume :

➪ Number of men are : $x$

Now, if 5 men less finishes the work in 20 more days.

So,

Number of men : $(x - 5)$

Number of days takes to finish the work :

= 20+40

= 60 days

Step 2 : Proportional analysis :

Since, the number of men are decreasing leads to increasing in the number of days to finish the work.

Therefore, it's a inverse proportion.

${ \underline{ \boldsymbol{According \: to \:the \: question : }}}$

$\implies (x - 5): 5 = 40 : 60$

$\implies \: \dfrac{(x - 5)}{x} = \dfrac{40}{60}$

$\implies 60(x - 5) = 40x$

$\implies 60x - 300 = 40x$

$\implies \: 60x - 40x = 300$

$\implies 20x = 300$

$\implies x = \dfrac{300}{20}$

$\implies x = \bf{{ 15}}$

$\therefore {\bf {\underline{There \: are \: 15 \: number \: of \: men\: }}}$

Know more :

Proportion : Proportion is an equality of a fraction.

Like :

$\to a : b :: c : d$

$\to \dfrac{a}{b} = \dfrac{c}{d}$