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 $16\frac{2}{3}$

Given $x$ is inversely proportional to $y$
Thus, $x=\frac{k}{y}$ where $k$ is constant or,

$\frac{x_1}{x_2}=\frac{y_2}{y_1}$

Let $x_1=100$ and $y_1=100$

Since $x_1$ is increased by $20\%$,

let $x_2=120$
Thus, $\frac{100}{120}=\frac{y_2}{100}$
$y_2=\frac{100\times 100}{120}=83\frac{1}{3}$
Therefore, decrease in $y_2=\frac{100-83.3}{100}\times 100=16\frac{2}{3}$
Hence, option 'B' is correct.