CEMC Cayley, 2026

Solution 1:

If $\dfrac{2m-n}{n}=\dfrac35$,
then $5(2m-n)=3n$ or $10m-5n=3n$. Simplifying, we get $10m=8n$ and so $\dfrac{m}{n}=\dfrac{8}{10}=\dfrac45$.

Solution 2:

If $\dfrac{2m-n}{n}=\dfrac35$,
then $\dfrac{2m}{n}-\dfrac{n}{n}=\dfrac35$ or
$\dfrac{2m}{n}-1=\dfrac35$.
Simplifying, we get $\dfrac{2m}{n}=\dfrac{8}{5}$, and so $\dfrac{m}{n}=\dfrac{8}{5}\times\dfrac12=\dfrac45$.