Observe the tables given below and in each one find whether x and y are proportional:

Question:

Observe the tables given below and in each one find whether x and y are proportional:

(i) 

Solution:

(i) Clearly, $\frac{x}{y}=\frac{3}{9}=\frac{5}{15}=\frac{8}{24}=\frac{11}{33}=\frac{26}{78}=\frac{1}{3}($ constant $)$

Therefore, $\mathrm{x}$ and $\mathrm{y}$ are proportional.

(ii) Clearly, $\frac{x}{y}=\frac{2.5}{10}=\frac{4}{16}=\frac{7.5}{30}=\frac{10}{40}=\frac{1}{4}$, while $\frac{14}{42}=\frac{1}{3}$

i. e., $\frac{2.5}{10}=\frac{4}{16}=\frac{7.5}{30}=\frac{10}{40}$ is not equal to $\frac{14}{42}$.

Therefore, $x$ and $y$ are not proportional.

(iii) Clearly, $\frac{x}{y}=\frac{5}{15}=\frac{7}{21}=\frac{9}{27}=\frac{25}{75}=\frac{1}{3}$, while $\frac{15}{60}=\frac{18}{72}=\frac{1}{4}$

i.e., $\frac{5}{15}=\frac{7}{21}=\frac{9}{27}=\frac{25}{75}$ is not equal to $\frac{15}{60}$ and $\frac{18}{72}$.

Therefore, $x$ and $y$ are not proportional.

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