If a: b = 4: 5 and b: c = 6: 7; find a: c. 

Given: 

a: b = 4: 5 and b: c = 6: 7

Now, a : b :: b : c = 4 : 5 :: 6 : 7

$$\begin{gathered} \Rightarrow \frac{\mathrm{a}}{\mathrm{b}} \times \frac{\mathrm{b}}{\mathrm{c}} = \frac{4}{5} \times \frac{6}{7} \\ \Rightarrow \frac{\mathrm{a}}{\mathrm{c}} =\frac{24}{35} \end{gathered}$$

So, a : c = 24 : 35