# Time to Complete a Work

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...

• 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. – Martin R Dec 10 '19 at 12:34
• @MartinR sorry.. will do from now on ... – techno Dec 11 '19 at 9:02

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.

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