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In Which of the Following Tables X and Y Vary Directly? - CBSE Class 8 - Mathematics

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Question

In which of the following tables x and y vary directly?

(i)

a 7 9 13 21 25
b 21 27 39 63 75

(ii)

a 10 20 30 40 46
b 5 10 15 20 23


(iii)

a 2 3 4 5 6
b 6 9 12 17 20


(iv)

a 12 22 32 42 52
b 13 23 33 43 53

Solution

\[\text{ If x and y vary directly, the ratio of the corresponding values of x and y remains constant}  . \]
\[(i)\]
\[\frac{x}{y} = \frac{7}{21} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{9}{27} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{13}{39} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{21}{63} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{25}{75} = \frac{1}{3}\]
\[\text{ In all the cases, the ratio is the same . Therefore, x and y vary directly } . \]
\[(ii)\]
\[\frac{x}{y} = \frac{10}{5} = 2\]
\[\frac{x}{y} = \frac{20}{10} = 2\]
\[\frac{x}{y} = \frac{30}{15} = 2\]
\[\frac{x}{y} = \frac{40}{20} = 2\]
\[\frac{x}{y} = \frac{46}{23} = 2\]
\[\text{ In all the cases, the ratio is the same . Therefore, x and y vary directly . } \]
\[(iii)\]
\[\frac{x}{y} = \frac{2}{6} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{3}{9} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{4}{12} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{5}{17} = \frac{5}{17}\]
\[\frac{x}{y} = \frac{6}{20} = \frac{3}{10}\]
\[\text{ In all the cases, the ratio is not the same . Therefore, x and y do not vary directly } . \]
\[(iv)\]
\[\frac{x}{y} = \frac{1^2}{1^3} = 1\]
\[\frac{x}{y} = \frac{2^2}{2^3} = \frac{1}{2}\]
\[\frac{x}{y} = \frac{3^2}{3^3} = \frac{1}{3}\]
\[\frac{x}{y} = \frac{4^2}{4^3} = \frac{1}{4}\]
\[\frac{x}{y} = $\frac{5^2}{5^3}$ = \frac{1}{5}\]
\[\text{ In all the cases, the ratio is not the same . Therefore, x and y do not vary directly . } \]
\[\text{ Thus, in (i) and (ii), x and y vary directly .} \]

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 8 by R D Sharma (2019-2020 Session) (2017 to Current)
Chapter 10: Direct and Inverse Variations
Ex. 10.1 | Q: 3 | Page no. 6

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Solution In Which of the Following Tables X and Y Vary Directly? Concept: Concept of Direct Proportion.
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