8 children and 12 men complete a certain piec | vedclass

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(D) Let the time taken by $1$ man to complete the work be $x$ days. Then,the time taken by $1$ child is $2x$ days.Since work is inversely proportional

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$12$

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(D) Let the time taken by $1$ man to complete the work be $x$ days. Then,the time taken by $1$ child is $2x$ days.Since work is inversely proportional to time,the efficiency of $1$ child is half the efficiency of $1$ man.Therefore,$1$ man $= 2$ children,or $1$ child $= 0.5$ men.Given that $8$ children and $12$ men complete the work in $9$ days.Converting children to men: $8$ children $= 8 	imes 0.5 = 4$ men.Total men $= 4 + 12 = 16$ men.So,$16$ men complete the work in $9$ days.Using the formula $M_1 D_1 = M_2 D_2$:$16 	imes 9 = 12 	imes D_2$$D_2 = \frac{16 	imes 9}{12} = \frac{144}{12} = 12$ days.Thus,$12$ men will finish the work in $12$ days.

$8$ children and $12$ men complete a certain piece of work in $9$ days. If each child takes twice the time taken by a man to finish the work,in how many days will $12$ men finish the same work?

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