\( \frac{p-2 q}{2 p+q}=\frac{2}{5} \) find the ratio \( p: q \)

To solve the equation \( \frac{p-2q}{2p+q}=\frac{2}{5} \), we can cross-multiply: \[ 5(p - 2q) = 2(2p + q) \] Expanding both sides gives us: \[ 5p - 10q = 4p + 2q \] Now, we rearrange the equation to isolate terms involving \( p \) and \( q \): \[ 5p - 4p = 10q + 2q \] This simplifies to: \[ p = 12q \] To find the ratio of \( p \) to \( q \), we can express it as: \[ \frac{p}{q} = 12 \] Thus, the ratio \( p : q = 12 : 1 \).