Question

Which of the following given set is in direct proportion?

• A. $\frac{7}{21},\frac{3}{9},\frac{2}{6},\frac{8}{24}$
• B. $\frac{3}{9},\frac{4}{12},\frac{6}{15},\frac{19}{38}$
• C. $\frac{2}{5},\frac{25}{10},\frac{20}{50},\frac{38}{95}$
• D. $\frac{6}{12},\frac{7}{15},\frac{9}{21},\frac{16}{24}$

Answer 1

The correct option is A $\frac{7}{21},\frac{3}{9},\frac{2}{6},\frac{8}{24}$

For a set to be in direct proportion,
the value of $\frac{x}{y}$ should be constant.

$\left(i\right)$
$\frac{7}{21},\frac{3}{9},\frac{2}{6},\frac{8}{24}$

$\frac{7}{21}=\frac{1}{3},\frac{3}{9}=\frac{1}{3},\frac{2}{6}=\frac{1}{3},\frac{8}{24}=\frac{1}{3}$
Here, $\frac{x}{y}$ is constant, so they are in direct proportion.

$\left(ii\right)$
$\frac{3}{9},\frac{4}{12},\frac{6}{15},\frac{19}{38}$

$\frac{3}{9}=\frac{1}{3},\frac{4}{12}=\frac{1}{3},\frac{6}{15}=\frac{2}{5},\frac{19}{38}=\frac{1}{2}$
Here, $\frac{x}{y}$ is not constant, so they are not in direct proportion.

$\left(iii\right)$
$\frac{2}{5},\frac{25}{10},\frac{20}{50},\frac{38}{95}$

$\frac{2}{5}=\frac{2}{5},\frac{25}{10}=\frac{5}{2},\frac{20}{50}=\frac{2}{5},\frac{19}{95}=\frac{2}{5}$
Here, $\frac{x}{y}$ is not constant, so they are not in direct proportion.

$\left(iv\right)$
$\frac{6}{12},\frac{7}{15},\frac{9}{21},\frac{16}{24}$

$\frac{6}{12}=\frac{1}{2},\frac{7}{15}=\frac{7}{15},\frac{9}{21}=\frac{3}{7},\frac{16}{24}=\frac{2}{3}$
Here, $\frac{x}{y}$ is not constant, so they are not in direct proportion.