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

Solution(By Examveda Team)

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