Question

Mark the correct alternative in the following question:

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

(a) 4 : 3 (b) 8 : 15 (c) 8 : 9 (d) 5 : 3

Answer 1

$$\begin{gathered} \mathrm{As},a:b=4:5 \\ \Rightarrow \frac{a}{b}=\frac{4}{5} \\ \mathrm{Also},b:c=2:3 \\ \Rightarrow \frac{b}{c}=\frac{2}{3} \\ \mathrm{So},a:c=\frac{a}{c} \\ =\frac{ab}{bc} \\ =\frac{a}{b}\times \frac{b}{c} \\ =\frac{4}{5}\times \frac{2}{3} \\ =\frac{8}{15} \\ =8:15 \end{gathered}$$

Hence, the correct alternative is option (b).