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I'm trying to solve the following question:

$15$ men and $16$ women together complete a piece of work in $6$ days. If $12$ women can complete the same project in $32$ days, in how many days will $10$ men complete the same project?

$(a)~12\\(b)~20\\(c)~16\\(d)~8\\(e)~14$

Why is this approach incorrect ?

$15x+16y=\frac16\\ 12y=\frac1{32}$

and solving...

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    $\begingroup$ As a 6 year member with >50 questions you should be able to format your question properly, instead of posting a screenshot and relying on others to do the MathJax for you. $\endgroup$ – Martin R Dec 10 '19 at 12:34
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    $\begingroup$ @MartinR sorry.. will do from now on ... $\endgroup$ – techno Dec 11 '19 at 9:02
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This approach is correct but you need to understand what $x$ and $y$ signify: $x$ is the fraction of the work a man does in $1$ day, and $y$ is the corresponding fraction for a woman. Thus, $10$ men complete $10x$ of the work in $1$ day, and finish the entire job in $1/(10x)=12$ days.

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  • $\begingroup$ Thanks..But solving the above equation does not yield correct results.. $\endgroup$ – techno Dec 11 '19 at 9:07
  • $\begingroup$ @techno $12$ is the correct answer, as obtained by these equations. If your textbook states some other answer, it could be an error. $\endgroup$ – Shubham Johri Dec 11 '19 at 10:02

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