Question

Given that y is inversely proportional to x. Complete the following table.

X Y 60 _

Y 7.5 _ 12

Answer 1

$\underline{\pink{ Inverse \:Proportion : }}$

Two quantities change in such a manner that, if one quantity increases , the other quantity decreases in same proportion and vice versa,is called inverse proportion.

$If \: x \: and \: y \:are \: in \: inverse \\ proportion\: then \: x \propto \frac{1}{y}$

$x = \frac{k}{y} , \: Where \:k\: is \: constant \\of \: proportionality$

$\blue{ xy = k }$

$Here, x_{1} = 60 , \: y_{1} = 7.5$

$and \: x_{2} = ? , y_{2} = 12$

$x_{2} \times y_{2} = x_{1} \times y_{1}$

$\implies x_{2} \times 12 = 60 \times 7.5$

$\implies x_{2} = \frac{ 60 \times 7.5 }{12}$

$\implies x_{2} = 5 \times 7.5$

$\implies x_{2} = 37.5$

Therefore.,

$\red{Value \: of \: x_{2} } \green { = 37.5}$

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