3 men and 5 womentogether can complete a work in 6 days, whereas 4 men and 9 womentogether can doit in 4 days. How many womenare required to do the same work in 7 days?

Let a man work of one day = $$\dfrac{1}{x }$$

and a women work of one day = $$\dfrac{1}{y}$$

then according to question $$\dfrac{3}{x} + \dfrac{5}{y} = \dfrac{1}{6}$$  ................ equestion (1)

and $$\dfrac{4}{x} +\dfrac {3}{y} = \dfrac{1}{4}$$           ................... equestion (2)

we multiply in question (1)by 4 and question (2 ) by 3 

$$\dfrac{12}{x} +\dfrac{20}{y} = \dfrac{4}{6} $$     ........ equestion(3)

$$\dfrac{12}{x}+\dfrac {27}{y} = \dfrac{3}{4}$$      ..........equestion (4)

we substract question (3) - euestion (4) 

then $$\dfrac{-7}{y} = \dfrac{-1}{12}$$

$$\Rightarrow\dfrac{7}{y} = \dfrac {1}{12}$$ remove - sign both side 

$$Rightarrow\dfrac{y}{7} = \dfrac {12}{1}$$

$$Rightarrow y = 84 

one women work in = 84 day

then 7 women  = $$\dfrac{84}{7}$$ = 12 days Ans