If a : b = 2 : 3 and b : c = 4 : 5, find a2 : b2 : bc = ?

Answer: Option B

$$\begin{array}{rl}& a:b=2:3\text{ and }b:c=4:5\\ & abc\\ & 2_{\times \left(4\right)}{3}_{\times \left(4\right)}\\ & 4_{\times \left(3\right)}{5}_{\times \left(3\right)}\\ & \overline{\underline{81215}}\\ & \therefore a^2:b^2:bc\\ & \Rightarrow {\left(8\right)}^2:{\left(12\right)}^2:\left(12\times 15\right)\\ & \Rightarrow 64:144:180\\ & \Rightarrow 16:36:45\end{array}$$