smc

Since there are $n$ women and $2n$ men, there are a total of $n+2n=3n$ players. Hence, the number of total matches must be $\left(\genfrac{}{}{0ex}{}{3n}{2}\right)=\frac{3n(3n-1)}{2}$. We also know that the ratio of the number of matches won by women to the number of matches won by men is $\frac{7}{5}$ and that there were no draws, so the total number of matches must be $(7+5)x=12x$ for some value $x$. This gives$$\frac{3n(3n-1)}{2}=12x$$So$$n(3n-1)=8x$$It follows that $n=8,4,3,2,1$ (various ways of splitting $8x$ into two factors). However, for solutions $n=4,2,1$, $x$ isn't an integer, therefore leaving solutions $n=8$ and $n=3$. $n=8$ is invalid. This can be shown as when $n=8$,$$\frac{24(23)}{2}=12x$$$$x=23$$The ratio of matches won by gender is $\frac{7x}{5x}=\frac{161}{115}$, so the number of matches won by women must be at least $161$. The maximum number of matches won by women is equivalent to the number of matches between men (generates 1 match won by men no matter the outcome) subtracted from the total number of matches, which is $\left(\genfrac{}{}{0ex}{}{24}{2}\right)-\left(\genfrac{}{}{0ex}{}{16}{2}\right)=156$. As the maximum number of matches won is smaller than $161$, the solution is extraneous/invalid. Hence, the answer must be $n=3$, or $\boxed{\text{none of these}}$