Question

If $\frac{m+n}{m+3n}=\frac{2}{3},$ find : $\frac{2n^2}{3m^2+mn}.$

Answer 1

$\frac{m+n}{m+3n}=\frac{2}{3}$

$\Rightarrow 3m+3n=2m+6n$

$\Rightarrow m=4n$

$\Rightarrow \frac{m}{n}=4⟶\left(1\right)$

Now,

$\frac{{2n}^2}{{3m}^2+mn}=\frac{{2n}^2}{3{\left(4n\right)}^2+\left(4n\right)n}=\frac{{2n}^2}{{48n}^2+{4n}^2}=\frac{2}{48+4}=\frac{2}{52}=\frac{1}{26}$