Question

If a : b = 4 : 5 and b : c = 2 : 3, then a : c = ...........

Answer 1

It is given that,
$\frac{a}{b}=\frac{4}{5}....\left(1\right)$
and
$\frac{b}{c}=\frac{2}{3}....\left(2\right)$

Now,
$$\begin{gathered} \frac{a}{c}=\frac{a÷b}{c÷b} \\ =\frac{a}{b}\times \frac{b}{c} \\ =\frac{4}{5}\times \frac{2}{3}\left[\mathrm{From}\left(1\right)\mathrm{and}\left(2\right)\right] \\ =\frac{8}{15} \end{gathered}$$

Hence, a : c = 8 : 15.