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

50 : 147
$latex \frac{a}{b} = \frac{5}{7}, \frac{c}{d} = \frac{2a}{3b}&s=1$
$latex => \frac{a}{b}\times\frac{c}{d} = \frac{5}{7}\times\frac{2a}{3b}&s=1$
$latex => \frac{ac}{bd} = \frac{10}{21}\times\frac{5}{7}&s=1$
$latex => \frac{ac}{bd} = \frac{50}{147}= 50 : 147&s=1$
Hence option [C] is the right answer.