10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

Explanation:-

$$\eqalign{ & 1\,woman's\,1\,day's\,work = \frac{1}{{70}} \cr & {\text{1}}\,{\text{child's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{140}} \cr & \left( {{\text{5}}\,{\text{women + 10}}\,{\text{children}}} \right){\text{'s}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{5}{{70}} + \frac{{10}}{{140}}} \right) = \left( {\frac{1}{{14}} + \frac{1}{{14}}} \right) = \frac{1}{7} \cr & \therefore {\text{5}}\,{\text{women}}\,{\text{and}}\,{\text{10}}\,{\text{chidren}}\,{\text{will}}\,{\text{complete}} \cr & {\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{7}}\,{\text{days}} \cr}$$