If A : B = 2 : 3, B : C = 2 : 4 and C : D = 2 : 5, then A : D is equal to -

Answer: Option D

$$\begin{array}{rl}& =\frac{\text{A}}{\text{B}}=\frac{2}{3},\frac{\text{B}}{\text{C}}=\frac{2}{4},\frac{\text{C}}{\text{D}}=\frac{2}{5}\\ & \Rightarrow \frac{\text{A}}{\text{D}}=\left(\frac{\text{A}}{\text{B}}\times \frac{\text{B}}{\text{C}}\times \frac{\text{C}}{\text{D}}\right)\\ & \Rightarrow \frac{2}{3}\times \frac{2}{4}\times \frac{2}{5}=\frac{2}{15}\\ & \Rightarrow \text{A}:\text{D}=2:15.\end{array}$$