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

If a : b = 5 : 7 and c : d = 2a : 3b, then ac : bd is:
[A]20 : 38
[B]50 : 151
[C]50 : 147
[D]10 : 21

50 : 147
\frac{a}{b} = \frac{5}{7},  \frac{c}{d} = \frac{2a}{3b}
=> \frac{a}{b}\times\frac{c}{d} = \frac{5}{7}\times\frac{2a}{3b}
=> \frac{ac}{bd} = \frac{10}{21}\times\frac{5}{7}
=> \frac{ac}{bd} = \frac{50}{147}= 50 : 147
Hence option [C] is the right answer.

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