Given that 24 carat gold is pure gold ; 18 carat gold is $\frac{3}{4}$ gold and 20 carat gold is $\frac{5}{6}$ gold, the ratio of the pure gold in 18 carat gold to the pure gold in 20 carat gold is

### Concept & Ratios of Fractions To find the ratio of two fractional quantities, we can simply divide one fraction by the other or multiply the first by the reciprocal of the second. ### Step-by-Step Solution * The pure gold content in 18 carat gold is given as $\frac{3}{4}$. * The pure gold content in 20 carat gold is given as $\frac{5}{6}$. * We need to find the ratio of pure gold in 18 carat gold to the pure gold in 20 carat gold. * Ratio = $\frac{3}{4} : \frac{5}{6}$ * To simplify, convert the ratio of fractions into a ratio of integers by cross-multiplying or multiplying by the LCM of the denominators (12): $$(\frac{3}{4} \times 12) : (\frac{5}{6} \times 12)$$ * $9 : 10$ ### Exam Strategy & Shortcut To quickly simplify a ratio of two fractions like $\frac{a}{b} : \frac{c}{d}$, use cross-multiplication: $(a \times d) : (b \times c)$. Here, it is $(3 \times 6) : (4 \times 5) = 18 : 20$, which simplifies directly to $9 : 10$. ### Common Pitfall Confusing the order of the ratio or forgetting to simplify the final ratio $18:20$ to its lowest terms. ### Final Answer Therefore, the correct answer is **9 : 10**.