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

ConceptConcept of Direct Proportion

#### 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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