If $${\text{A}}$$ : $${\text{B}}$$ = $$\frac{1}{2}$$ : $$\frac{3}{8}{\text{,}}$$  $${\text{B}}$$ : $${\text{C}}$$ = $$\frac{1}{3}$$ : $$\frac{5}{9}$$ and $${\text{C}}$$ : $${\text{D}}$$ = $$\frac{5}{6}$$ : $$\frac{3}{4}{\text{,}}$$  Then the ratio of A : B : C : D is ?
a) 6 : 4 : 8 : 10
b) 6 : 8 : 9 : 10
c) 8 : 6 : 10 : 9
d) 4 : 6 : 8 : 10

Answer: c
Explanation:
$$\eqalign{ & {\text{A}}:{\text{B}} = \frac{1}{2}:\frac{3}{8}, \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{4}{3} \cr & {\text{B}}:{\text{C}} = \frac{1}{3}:\frac{5}{9}, \cr & \frac{{\text{B}}}{{\text{C}}} = \frac{1}{3} \times \frac{9}{5} = \frac{3}{5} \cr & {\text{C}}:{\text{D}} = \frac{5}{6}:\frac{3}{4}, \cr & \frac{{\text{C}}}{{\text{D}}} = \frac{{5 \times 4}}{{6 \times 3}} = \frac{{10}}{9} \cr & {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & {\text{4}}:{\text{3}} \cr & \,\,\,\,\,\,\,{\text{3}}:{\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ 10}}:{\text{9}} \cr & \Rightarrow {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & \,\,\,\,\,\,\,\,\,8:6:10:9 \cr} $$