Question

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

• A. 20
• B. $16\frac{2}{3}$
• C. 5
• D. $1\frac{9}{11}$

Answer 1

The correct option is B

$16\frac{2}{3}$

$x\propto \frac{1}{y}$
$x=\frac{k}{y}$, k =constant
$\Rightarrow y=\frac{k}{x}$
When x increases by 20%
$x^{\prime }=x+\frac{20\left(x\right)}{100}=\frac{6x}{5}{y}^{\prime }=\frac{k}{\left(\frac{6x}{5}\right)}=\frac{5k}{6x}$
Change in $y=\frac{5k}{6x}-\frac{k}{x}=\frac{-k}{6x}$

$\therefore$ Value of y decreases
% decrease in $y=\frac{\frac{k}{6x}}{\frac{k}{x}}\times 100$
$=\frac{1}{6}\times 100=\frac{50}{3}=16\frac{2}{3}$