A recipe calls for flour and sugar in a ratio of 5:2. If 20 cups of flour are used, how many cups of sugar are needed?

The ratio of flour to sugar is $5:2$, so $\frac{\text{flour}}{\text{sugar}}=\frac{5}{2}$. With $20$ cups of flour, $\frac{5}{2}=\frac{20}{x}$, so $5x=40$ and $x=8$ cups of sugar, choice B. The flour was multiplied by $4$ ($5\to20$), so the sugar must also be multiplied by $4$ ($2\to8$). Choice A ($4$) multiplies by $2$. Choice C ($10$) is half of the flour. Choice D ($50$) inverts the ratio, $\frac{20\cdot5}{2}$. Sugar should be less than flour, since the ratio has the smaller number on the sugar side.