Question

16 men are able to complete a piece of work in 12 days working 14 hour in a day how long will 28 men working 12 hours a day take to complete the work

Answer 1

16×12×14=28×12×x
x=8 days

Answer 2

$Here , we \:have \:three \: quantities \: i.e., \\number \:of \: men , \: number \:of \:hours \:per\\day \:and \: number \:of \:days$

$\blue { ( Number \:of \:men \propto compound } \\\blue{ ratio \:of \: inverse \:ratio \:of }\\\blue { number \:of \:hours \:per \:day \:and} \\\blue { inverse \:ratio \:of \: number \:of \:days)}$

$\begin {tabular} { |c|c|c| } </p><p>\cline {1-3} No.of men(M)&No.of hours per day (H)&No. of days (D) \\</p><p>\cline {1-3} 16&14&12\\</p><p>\cline {1-3} 28&12&? \\</p><p>\cline {1-3} </p><p>\end {tabular}$

$Here, M_{1} = 16, \: H_{1} = 14 , \: D_{1} = 12$

$and , M_{2} = 28, \: H_{2} = 12 , \: D_{2} = \red{?}$

$\boxed {\pink { M_{2} \times H_{2} \times D_{2} = M_{1} \times H_{1} \times D_{1} }}$

$\implies 28 \times 12 \times D_{2} = 16 \times 14 \times 12$

$\implies D_{2} = \frac{ 16 \times 14 \times 12}{28 \times 12 }$

$\implies D_{2} = 8 \:days$

$Hence , \red { Number \: of \:days \:to }\\\red{ complete\: the \: work } \green {= 8\:days }$

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