Question

# If a : b = 8 : 9, b : c = 18 : 40, then a : c isA. 1 : 5B. 5 : 2C. 2 : 5D. None

Hint:To solve this question, we will find the value of a and c in terms of b and then take their ratios to get the required value. We can find the values of a and c in terms of b by using cross multiplication.

\begin{align} & \dfrac{a}{b}=\dfrac{8}{9} \\ & \Rightarrow a=\dfrac{8}{9}b \\ \end{align}
\begin{align} & \dfrac{b}{c}=\dfrac{18}{40} \\ & \Rightarrow c\times 18=b\times 40 \\ & \Rightarrow c=\dfrac{40}{18}b \\ \end{align}
\begin{align} & \dfrac{a}{c}=\dfrac{\dfrac{8}{9}b}{\dfrac{40}{18}b} \\ & \Rightarrow \dfrac{a}{c}=\dfrac{8\times 18}{9\times 40} \\ & \Rightarrow \dfrac{a}{c}=\dfrac{144}{360} \\ & \Rightarrow \dfrac{a}{c}=\dfrac{2}{5} \\ \end{align}
Note: In this question, since we have the ratios of $\dfrac{a}{b},\dfrac{b}{c}$ , we can also get the ratio of $\dfrac{a}{c}$ by multiplying these ratios, which is a shorter way to get the answer and save time. The students sometimes take a = 8 and c = 40 from the given ratios and end up getting $\dfrac{a}{c}=\dfrac{1}{5}$ , which is also present in the option, but this method as well as the answer is incorrect, so we should be careful not to do this mistake while solving such questions.