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  4. If 5 men and 6 women can do a piece of work in 5 days, 3 men and 4 women can do the same work in 8 days, then in how many days can 7 men and 6 women complete the work?

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Q. If 5 men and 6 women can do a piece of work in 5 days, 3 men and 4 women can do the same work in 8 days, then in how many days can 7 men and 6 women complete the work?

Time and Work, Pipes and Cisterns

Solution:

Given $(5 m+6 w)$ one day's work $=\frac{1}{5}$
$(3 m+4 w) \text { one day's work }=\frac{1}{8} $
$\Rightarrow(5 m+6 w) 5=(3 m+4 w) 8$
$25 m+30 w=24 m+32 w $
$m=2 w$
Required number of days
$=\frac{25 m+30 w}{7 m+6 w} $=\frac{25(2 w)+30 w}{7(2 w)+6 w}=\frac{80 w}{20 w}=4 \text { days }$