Explanation:

To find the value of (2x + 4y) : (x + 4y), we'll follow these steps:

- Given Ratio: x : y = 1 : 2

- Express x in terms of y: x = y/2

- Substitute this into the expression (2x + 4y) : (x + 4y).

- Calculate:

- $2x+4y=2(\frac{y}{2})+4y=y+4y=5y$

- $x+4y=\frac{y}{2}+4y=\frac{y}{2}+\frac{8y}{2}=\frac{9y}{2}$

- Find the ratio:

- $\frac{5y}{\frac{9y}{2}}=\frac{5y\times 2}{9y}=\frac{10y}{9y}=\frac{10}{9}$

- Answer:

- The ratio is 10 : 9

Options:

1. 10 : 9: Correct!

2. 8 : 7

3. 5 : 4

4. 9 : 8