Question

The relation between two different sets of variables is shown. Which of the following is correct?

$A$	$1$	$2$	$6$	$12$
$B$	$3$	$6$	$18$	$36$

$C$	$1$	$4$	$10$	$12$
$D$	$2$	$5$	$14$	$20$

• A. $A\text{and}B$ represent a proportional relationship.
• B. $C\text{and}D$ represent a non-proportional relationship.
• C. None of the above
• D. Both option $\left(A\right)\text{and option}\left(B\right)$ are correct.

Answer 1

The correct option is D Both option $\left(A\right)\text{and option}\left(B\right)$ are correct.

Two quantities $x$ and $y$ are said to be in a proportional relationship if their ratio at every point is always the same.

For the first set of variables, $A\text{and}B$:

$A$	$1$	$2$	$6$	$12$
$B$	$3$	$6$	$18$	$36$

The ratio of the quantities $A\text{and}B$

at the first point $=\frac{1}{3}$,

at the second point $=\frac{2}{6}=\frac{1}{3}$,

at the third point $=\frac{6}{18}=\frac{1}{3}$, and

at the fourth point $=\frac{12}{36}=\frac{1}{3}$.

So, we can observe that the ratio of the two quantities, $A\text{and}B$, at each point is the same.
Hence, the quantities $A\text{and}B$ represent a proportional relationship.

For the first set of variables, $C\text{and}D$:

$C$	$1$	$4$	$10$	$12$
$D$	$2$	$5$	$14$	$20$

The ratio of the quantities $C\text{and}D$

at the first point $=\frac{1}{2}$,

at the second point $=\frac{4}{5}$,

at the third point $=\frac{10}{14}=\frac{5}{7}$, and

at the fourth point $=\frac{12}{20}=\frac{3}{5}$.

So, we can observe that the ratio of the two quantities, $C\text{and}D$, at each point is not the same.
Hence, the quantities $C\text{and}D$ do not represent a proportional relationship, or in other words, they represent a non-proportional relationship.

Option $C$ is correct.