Question

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

• A. $20:38$
• B. $50:147$
• C. $10:21$
• D. $50:151$

Answer 1

The correct option is B $50:147$

$\frac{a}{b}=\frac{5}{7},\frac{c}{d}=\frac{2a}{3b}=\frac{2}{3}\times \frac{a}{b}=\frac{2}{3}\times \frac{5}{7}=\frac{10}{21}$

$\therefore \frac{a}{b}\times \frac{c}{d}=\frac{5}{7}\times \frac{10}{21}\Rightarrow \frac{ac}{bd}=\frac{50}{147}$

$\Rightarrow ac:bd=50:147$.