Question

If $A:B=2:3$ and $B:C=4:5$ then $C:A=?$

• A. $6:8$
• B. $8:15$
• C. $8:5$
• D. $15:8$

Answer 1

The correct option is D

$15:8$

As it is given that, $A:B=2:3$ and $B:C=4:5$

$$\begin{gathered} A:B=2:3 \\ \Rightarrow \frac{A}{B}=\frac{2}{3} \\ \Rightarrow A=\frac{2B}{3} \end{gathered}$$

Also, $B:C=4:5$

$$\begin{gathered} \frac{B}{C}=\frac{4}{5} \\ \frac{C}{B}=\frac{5}{4} \\ \Rightarrow C=\frac{5B}{4} \end{gathered}$$

Now, $\frac{C}{A}=\frac{{\displaystyle \frac{5B}{4}}}{{\displaystyle \frac{2B}{3}}}=\frac{5B}{4}\times \frac{3}{2B}=\frac{15}{8}$

$\Rightarrow$$C:A=15:8$

Hence, correct option is $\left(b\right)$.