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1. 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

Solution:

\begin{aligned} \frac{A}{D} = \frac{A}{B} \times \frac{B}{C} \times \frac{C}{D} \\ = \frac{2}{3} \times \frac{4}{5} \times \frac{5}{9} \\ = \frac{2 \times 4 \times 5}{3 \times 5 \times 9} \\ = \frac{8}{27} \\ = 8 : 27 \end{aligned}

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