Question

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

Answer 1

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

$\bold\pink{Given:}$

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

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

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

$\bold\pink{Solution:}$

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

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

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

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

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

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

$\sf {→30 \times 40 = 20X_{2}}$

$\sf{→1200 = 20X_{2}}$

$\sf {→ \dfrac {1200}{20} = X_{2}}$

$\sf {→ 60 = X_{2}}$

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