Question
Answers

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

Answer Verified Verified
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.

Complete step-by-step answer:
We have been given that, a : b = 8 : 9, b : c = 18 : 40 and have been asked to find the value of a : c. As we can see, both the ratios contain b, so we will try to find the value of a and c in terms of b. So, if we take the first set, that is, a : b = 8 : 9, then we know that it can be written as,
 $ \begin{align}
  & \dfrac{a}{b}=\dfrac{8}{9} \\
 & \Rightarrow a=\dfrac{8}{9}b \\
\end{align} $
Similarly, we can write the other set, that is, b : c = 18 : 40 as,
 $ \begin{align}
  & \dfrac{b}{c}=\dfrac{18}{40} \\
 & \Rightarrow c\times 18=b\times 40 \\
 & \Rightarrow c=\dfrac{40}{18}b \\
\end{align} $
So, we have obtained the values of a and c in terms of b. Now, we have to find a : c. Therefore, we will get a : c as,
 $ \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} $
Hence, we get the ratio of a : c as 2 : 5.
Therefore, the correct answer is option C.

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.
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