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

Answer: Option B

$$\begin{array}{rl}& \text{a}:\text{b}\text{c}:\text{d}\\ & 5:72\text{a}:3\text{b}\\ & \frac{a}{b}=\frac{5}{7},\frac{c}{d}=\frac{2a}{3b}\\ & =\frac{2}{3}\times \frac{5}{7}\\ & =\frac{10}{21}\\ & \therefore ac:bd\\ & =\frac{\text{ac}}{\text{bd}}\\ & =\frac{5}{7}\times \frac{10}{21}\\ & =\frac{50}{147}\\ & =50:147\end{array}$$