Question

A place of work is done by $6$ men & $5$ women in $6$ day or $3$ men and $4$ women in $10$ days. How many days will it take for $9$ men & $15$ women to finish that work ?

Answer 1

we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work =x
and 1 woman 1 day work = y.
$6x+5y=\frac{1}{6}........\left(1\right)$

$3x+4y=\frac{1}{10}........\left(2\right)$
On solving (1) and (2) to, we get

$x=\frac{1}{54}andy=\frac{1}{90}$

Hence, (9 men + 15 women)'s 1 days work

$=9x+15y$

$=9\times \frac{1}{54}+15\times \frac{1}{90}$

$=\frac{1}{6}+\frac{1}{6}$

$=\frac{2}{6}$

$=\frac{1}{3}ans.$
Then, 9 men and 15 women will finish the work in 3 days