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Standard VIII

Mathematics

Inverse Proportion

If x varies...

Question

If $x$ varies inversely as $y$ and $x = 7$ when $y = 9$ .
(a) Find constant of variation $k$ .
(b) Write equation of variation.
(c) Find $y$ when $x = 9$ .

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Solution

(a) $x \propto \frac{1}{y}$
$\Rightarrow x = \frac{k}{y}$
$\Rightarrow 7 = \frac{k}{9}$
$\Rightarrow k = 7 \times 9$
$∴ k = 63$

(b) $x = \frac{63}{y}$

(c) $y = \frac{63}{x}$
$\Rightarrow y = \frac{63}{9}$
$∴ y = 7$ .

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If x varies inversely as y and x=7 when y=9.(a) Find constant of variation k.(b) Write equation of variation.(c) Find y when x=9.

(a) x∝1y⇒x=ky⇒7=k9⇒k=7×9∴k=63(b) x=63y(c) y=63x⇒y=639∴y=7.

If $x$ varies inversely as $y$ and $x = 7$ when $y = 9$ .
(a) Find constant of variation $k$ .
(b) Write equation of variation.
(c) Find $y$ when $x = 9$ .

(a) $x \propto \frac{1}{y}$
$\Rightarrow x = \frac{k}{y}$
$\Rightarrow 7 = \frac{k}{9}$
$\Rightarrow k = 7 \times 9$
$∴ k = 63$

(b) $x = \frac{63}{y}$

(c) $y = \frac{63}{x}$
$\Rightarrow y = \frac{63}{9}$
$∴ y = 7$ .