If A : B = 2 : 3, B : C = 4 : 5 and C : D = 5 : 9 then A : D is equal to:

A. 11 : 17

B. 8 : 27

C. 5 : 9

D. 2 : 9

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & \frac{A}{D} = {\frac{A}{B}} \times {\frac{B}{C}} \times {\frac{C}{D}} \cr & \,\,\,\,\,\,\,\,\, = {\frac{2}{3}} \times {\frac{4}{5}} \times {\frac{5}{9}} \cr & \,\,\,\,\,\,\,\,\, = \frac{{ {2 \times 4 \times 5} }}{{ {3 \times 5 \times 9} }} \cr & \,\,\,\,\,\,\,\,\, = \frac{8}{{27}} \cr & \,\,\,\,\,\,\,\,\, = 8:27 \cr} $$