In a business, the ratio of the capitals of A and B is 2 : 1, that of B and C is 4 : 3 and that of D and C is 6 : 5. Then the ratio of the capitals of A and D is -

$$\eqalign{ & = \frac{{\text{A}}}{{\text{B}}} = \frac{2}{1},\,\,\frac{{\text{B}}}{{\text{C}}} = \frac{4}{3},\,\,\frac{{\text{C}}}{{\text{D}}} = \frac{5}{6} \cr & \Rightarrow \frac{{\text{A}}}{{\text{D}}} = \left( {\frac{{\text{A}}}{{\text{B}}} \times \frac{{\text{B}}}{{\text{C}}} \times \frac{{\text{C}}}{{\text{D}}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{2}{1} \times \frac{4}{3} \times \frac{5}{6}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{9} \cr & \Rightarrow {\text{A}}:{\text{D}} = {\text{20}}:{\text{9}} \cr} $$