4 : 15
Explanation:[tex]\begin{gathered} \text{x : y = 2: 5} \\ \frac{x}{y}\text{ = }\frac{2}{5} \\ \\ 2x\text{ : 3y = ?} \end{gathered}[/tex][tex]\begin{gathered} 2x\colon\text{ 3y = }\frac{2x}{3y} \\ 2x\colon3y\text{ = }\frac{2}{3}\times\frac{x}{y} \end{gathered}[/tex][tex]\begin{gathered} \text{substitute for x/y in 2x:3y} \\ \frac{2}{3}\times\frac{x}{y}\text{ =}\frac{2}{3}\times\frac{2}{5} \\ =\text{ }\frac{4}{15} \\ \\ \text{Hence, 2x:3y = }\frac{4}{15} \\ or \\ 4\colon15 \end{gathered}[/tex]