Question

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. $1\frac{9}{11}$

Answer 1

The correct option is A $20$

For inversely proportional numbers, the product of that numbers must be constant.

Let $x\times y=k=$constant

Let us take $x,y$ as $10$

$\therefore x\times y=100$

If x increases by $20\%$ i.e $x=12$, but the product remains constant i.e. $400$.

$\therefore 12\times y=100$

$⟹y=\frac{100}{12}$

In percentage $y=\frac{(10-\frac{100}{12})}{10}\times 100=\frac{20}{12\times 10}\times 100=\frac{200}{12}=\frac{50}{3}=16\frac{2}{3}$.

Hence, option B is correct.