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1. If a : b = 5 : 7 and c : d = 2a : 3b then ac : bd is = ?

A. 20 : 38

B. 50 : 147

C. 10 : 21

D. 50 : 151

Solution:

\begin{aligned} a : b c : d \\ 5 : 7 2 a : 3 b \\ \frac{a}{b} = \frac{5}{7}, \frac{c}{d} = \frac{2 a}{3 b} \\ = \frac{2}{3} \times \frac{5}{7} \\ = \frac{10}{21} \\ ∴ a c : b d \\ = \frac{ac}{bd} \\ = \frac{5}{7} \times \frac{10}{21} \\ = \frac{50}{147} \\ = 50 : 147 \end{aligned}

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