$4$ men and $6$ women can finish a work in $8$ days and $3$ men and $7$ women can do the same work in $10$ days. In how many days will $10$ women do the same work.

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Solution

Let the work done in 1 day by a man,woman is $\frac{x}{a}, \frac{x}{b}$ if the total work is $x$ .
$\frac{4 x}{a} + \frac{6 x}{b} = \frac{x}{8}; \frac{3 x}{a} + \frac{7 x}{b} = \frac{x}{10} ⟹ b = 11 a; b = 400$
$\frac{10 x}{b} = \frac{x}{t} ⟹ t = 40$

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