Two positive numbers x and y are inversely proportional. If x increases by 20%, then the percentage decrease in y is

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24 सित॰, 2022

Table of content

Two positive numbers $x$ and $y$ are inversely proportional. If $x$ increases by $20 %$ , then the percentage decrease in $y$ is

A

$20$

B

$16 \frac{2}{3}$

C

$5$

D

$1 \frac{9}{1 1}$

Solution

Correct option is A)

For inversely proportional numbers, the product of that numbers must be constant.
Let $x \times y = k =$ constant
Let us take $x, y$ as $10$
$∴ x \times y = 100$
If x increases by $20 %$ i.e $x = 12$ , but the product remains constant i.e. $400$ .
$∴ 12 \times y = 100$
$⟹ y = \frac{1 0 0}{1 2}$
In percentage $y = \frac{( 1 0 - \frac{1 0 0}{1 2} )}{1 0} \times 100 = \frac{2 0}{1 2 \times 1 0} \times 100 = \frac{2 0 0}{1 2} = \frac{5 0}{3} = 16 \frac{2}{3}$ .
Hence, option B is correct.