5 men and 4 women can do a piece of work in 12 days, while 4 men and 5 women can do the same piece of work in 10 days. In how many days can 5 men and 2 women do the same piece of work?
Solution
Given:
5 men and 4 women 1 day work = $\dfrac{1}{12}$ and,
4 men and 5 women 1 day work = $\dfrac{1}{10}$
$\Rightarrow$ (5 men + 4 women)$\times 12$ = (4 men +5 women) $\times 10$
$\Rightarrow$ 60 men + 48 women = 40 men + 50 women
$\Rightarrow$ 20 men = 2 women
$\Rightarrow$ 10 men = 1 woman
Therefore, 5 men + 2 women = 5 men + 20 men = 25 men
$M_1 D_1 = M_2 D_2$
$45 \times 12 = 25 \times D_2$
$D_2 = \dfrac{108}{5}=21\dfrac{3}{5} $ days