If $\dfrac {m+n}{m+3n}=\dfrac {2}{3}$, find: $\dfrac {60n^{2}}{3m^{2}+mn}$.

#### Solution

$\dfrac{m+n}{m+3n}=\dfrac{2}{3}$
$3m+3n=2m+6n$
$m=3n$ (1)
$\dfrac{60n^{2}}{3m^{2}+mn}=\dfrac{60n^{2}}{3(3n)^{2}+(3n)n}=\dfrac{60n^{2}}{27n^{2}+3n^{2}}=\dfrac{60n^{2}}{30n^{2}}=2$
Hence the correct answer is 2.