4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Explanation:-

$$\eqalign{ & {\text{Let}}\,{\text{1}}\,{\text{man's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = x\,{\text{and}} \cr & {\text{1}}\,{\text{woman's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = y \cr & {\text{Then}},\,4x + 6y = \frac{1}{8}\,{\text{and}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3x + 7y = \frac{1}{{10}} \cr & {\text{Solving}}\,{\text{the}}\,{\text{two}}\,{\text{equations,}}\,{\text{we}}\,{\text{get}} \cr & x = \frac{{11}}{{400}}\,\,,\,\,\,y = \frac{1}{{400}} \cr & \therefore {\text{1}}\,{\text{woman's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{400}} \cr & \Rightarrow {\text{10}}\,{\text{women's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{{400}} \times 10} \right) = \frac{1}{{40}} \cr & {\text{Hence,}}\,{\text{10}}\,{\text{women}}\,{\text{will}}\,{\text{complete}}\,{\text{thw}}\,{\text{work}}\,{\text{in}}\,{\text{40}}\,{\text{days}} \cr}$$