Question

A:B equal 5:7 and c:d equal2a:3b then ac:bd will be

Answer 1

Step-by-step explanation:

$Given: \\ </p><p>a : b=5 :7 \\ \\ \implies \: \frac{a}{b} = \frac{5}{7} \\\\ \implies \: \boxed{a = \frac{5}{7} b} ....(1) \\ \\ c : d = 2a : 3b \\ \\ \implies \: \frac{c}{d} = \frac{2a}{3b} = \frac{2}{3} \times \frac{a}{b} = \frac{2}{3} \times \frac{5}{7} \\ \\ \implies \: \frac{c}{d} = \frac{10}{21}\\ \\ \implies \boxed {c = \frac{10}{21}d}....(2) \\ \\ now \: \\\huge {ac: bd= \frac{ac}{bd}} \\\\\huge{=\frac{\frac{5}{7}b\times \frac{10}{21}d}{bd}} \\\\\huge{=\frac{\frac{5\times 10}{7\times 21}bd}{bd}} \\\\\huge {= \frac{\frac{50}{147}}{1}} \\\\\huge {=\frac{50}{147}} \\\\</p><p>Thus\: \\\huge {ac: bd= \frac{50}{147}}$