Question

if 40 men can finish a piece of work in 30 days how many days 20 men to do it​

Answer 1

Correct question:

If 40 men can finish a piece of work in 30 days, then how many days 20 men will take to complete the same piece of work?

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Given:

• 40 men can finish a piece of work in 30 days.

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To find:

• Number of days 20 men will take to complete the same piece of work.

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$\boxed {\sf {\large {Understanding\ the\ question}}}$

Here the concept of inverse proportion is used. Meaning as one quantity increases, the other quantity decreases.

In this question (see the table), as the number of men decreases, the number of days will increase, because less men will take more time to finish the work, therefore it is in inverse proportion.

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Solution:

For inverse proportion,

$\sf {X_{1} Y_{1} = X_{2} Y_{2}}$

$\implies \sf {30 \times 40 = 20X_{2}}$

$\implies \sf {1200 = 20X_{2}}$

$\implies \sf {\dfrac {1200}{20} = X_{2}}$

$\boxed {\bf {\red {60\ days = X_{2}}}}$

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Final answer:

20 men will take 60 days to complete the same piece of work.

Answer 2

$\sf\fcolorbox{gray}{white}{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:Answer\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

$\bold\pink{Given:}$

$\sf\color{navy}{40 \: men \: can \: finish \: a \:piece \: of \:work \: in \:30 \: days}$

$\bold\pink{To\: find:}$

$\sf\color{navy}{Number \:of\: days\: 20 \:men\: will \:take\: to}$ $\sf\color{navy}{complete\: the\:same \:piece \:of \:work}$

$\bold\pink{Solution:}$

$\tiny\boxed{\begin{array}{cc} \: \sf Number \: of \: days& \sf Number \: of \: men \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}& \\\sf 30&\sf 40 \\\ \\ \sf ? &\sf 20 &\sf \end{array}}$

$\sf\color{navy}{We \: can \: see \: that, \: it \:is \:in \: inverse \: proportion}$

$\sf{For \:inverse \: proportion:}$

$\small\underline{\boxed{\sf\;\;Formula\: used}}$

$\sf{X_{1} Y_{1} = X_{2} Y_{2}}$

$\sf\color{navy}{Substituting\: values\:in\:the\:formula:}$

$\sf {→30 \times 40 = 20X_{2}}$

$\sf{→1200 = 20X_{2}}$

$\sf {→ \dfrac {1200}{20} = X_{2}}$

$\sf {→ 60 = X_{2}}$

$\sf\color{navy}{Hence,}$ $\sf\color{navy}{20 \:men \:will\: take\: 60\: days \:to \:complete \:the\: }$ $\sf\color{navy}{same\:piece \:work}$