Question

$a$ and $b$ are inversely proportional to each other and are positive. If $a$ increase by $100$, the $b$ decrease by

• A. $50$
• B. $75$
• C. $100$
• D. $200$

Answer 1

Answer: (A)

$50$

$a\alpha \frac{1}{b}\Rightarrow a=\frac{k}{b}$

When a increases by $100\%$

$\therefore a+a\times \frac{{}_{100}}{100}=2a$

then, $2a=\frac{k}{b^{\prime }}\Rightarrow b^{\prime }=\frac{k}{2a}$

$\%$ decrease in $b=\left(\frac{b^{\prime }-b}{b}\right)\times 100$

$=\left(\frac{\frac{k}{2a}-\frac{k}{a}}{\frac{k}{a}}\right)\times 100$

$=50\%$

Correct option is (A).