At the Andromeda Book Store, the ratio of self-help titles to fiction titles is $3:10$, and the ratio of biography titles to fiction titles is $2:7$. What is the ratio of biography titles to self-help titles?

Simple ratios can be expressed as fractions. For instance, $\frac{\text{ Self-help titles }}{\text{ Fiction titles }}=\frac{3}{10}$ and $\frac{\text{ Biography titles }}{\text{ Fiction titles }}=\frac{2}{7}$ Now note that we can get the ratio we want by just multiplying two wellchosen fractions: $\frac{\text{ Biography titles }}{\text{ Fiction title }}\times \frac{\text{ Fiction titles }}{\text{ Self-help titles }}=\frac{\text{ Biography titles }}{\text{ Self-help titles }}$ Note that we have to "flip" one of the ratios to do the calculation: $\frac{\text{ Biography titles }}{\text{ Fiction titles }}\times \frac{\text{ Fiction titles }}{\text{ Self-help titles }}=\frac{2}{7}\times \frac{10}{3}=\frac{20}{21}$ Therefore, the correct answer is B.