3 women and 18 children together take 2 days | vedclass

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(D) Let the work done by $1$ woman in $1$ day be $W$ and by $1$ child in $1$ day be $C$.Given that $6$ women complete the work in $3$ days,the total w

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$6$

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(D) Let the work done by $1$ woman in $1$ day be $W$ and by $1$ child in $1$ day be $C$.Given that $6$ women complete the work in $3$ days,the total work is $6 	imes 3 = 18$ units (in terms of woman-days).Thus,$1$ woman's $1$ day work $= 1/18$ of the total work.Given that $3$ women and $18$ children complete the work in $2$ days,their combined $1$ day work is $1/2$.So,$3(1/18) + 18C = 1/2$.$1/6 + 18C = 1/2$.$18C = 1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3$.$C = 1/(3 	imes 18) = 1/54$.This means $1$ child completes $1/54$ of the work in $1$ day.Therefore,$9$ children will complete $9 	imes (1/54) = 9/54 = 1/6$ of the work in $1$ day.To complete the whole work,$9$ children will take $1 / (1/6) = 6$ days.

$3$ women and $18$ children together take $2$ days to complete a piece of work. How many days will $9$ children alone take to complete the piece of work,if $6$ women alone can complete the piece of work in $3$ days?

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